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Class 8 math chapter 3 creative question with solution

Creative Questions and Answers Question no : 01 The length of a rectangular garden is 60 metres and breadth is 40 metres. There is a road of width 2 metres inside around the garden. a. Find the area of the garden in square centimetre. b. Find out the area of the road. c. Find the perimeter of a rectangular region whose length is 6 times its breadth and area is equal to the rectangle given in the stem. Solution: (a) Here given for a rectangular garden, length = 60 m = 6000 cm and breadth = 40 m = 4000 cm ∴ Area of the garden = 6000 × 4000 sq.cm = 24000000 sq. cm (b) From (a) above the area of the rectangular garden,

ABCD, shown above is 24000000 sq. cm or 2400 sq. m including road. Again, the length of the garden excluding road = (60 - 4) m = 56 m and the breadth of the garden excluding road = (40 - 4) m = 36 m ∴ area of the garden excluding road = 56 x 36 sq. m = 2016 sq. m ∴ area of the road = (2400 – 2016 ) sq. m = 384 sq m. So, the required area of road is 384 sq. m. (c) Let the breadth of the proposed rectangular region be 'x' m. ∴ It’s length is 6x m ∴its area is 6x × x sq. m or 6x² sq. m Now according to the given information, 6x² = 2400, the area of the rectangle mentioned in (b) above or, x² = 400 or; x = 20 and 6x = 6 × 20 or, 120 That is, the length of the proposed rectangular region is 120 m and breadth is 20 m, ∴ The perimeter of the rectangular region = 2(length + breadth) = 2(120 + 20) m = 2(120 +20)m = 2(140) m = 280 m. So, The required perimeter of the proposed square region is 280 m. Question no : 02

In figure, ABCD is a rectangular garden and there is a 1 metre wide road inside around the garden. Solution: a. Determine the area of rectangular garden by triangle. b. Determine the area of the road. c. There is a three metres wide road around the outside of a square land which perimeter is equal to the rectangular garden mentioned in the figure. How much money will be spent to planting grass at Tk. 7.00 per sq. metre? (a) According to the given stem, rectangle ABCD = 2 ×△ACD = 2 × × 40 x 30 sq. m = 1200 sq. m So, the area of the garden is 1200 sq. m. (b) From the stem, area of the garden with road = 40 x 30 sq. cm = 1200 sq. cm Again, the length of the garden without road = ( 40 - 1 × 2) m = 38m And the breadth of the garden without road = (30 – 1 × 2) m = 28 m. ∴area of the garden without road = 28 × 38 sq. m = 1064 sq. m ∴area of the road = (1200–1064) sq. m = 136 sq. m, (c) Here we have, perimeter of the rectangle = 2(40 + 30) m = 140 m Now according to the stem, perimeter of a square = 140 m ∴ length of each side of the square = = 35 m So, the area of the square = 35 x 35 sq. m = 1225 sq. m Again, length of each side of the square with 3m wide road around outside the square = (35 +3 + 3) m = 41 m. ∴area of the square with road = 41 x 41 = 1681 sq. m So, area of the road = (1681– 1225) = 456 sq. m. Now we have, cost of planting grass = Tk. 7 per sq. m ∴ ” ” ” ” in 456 sq. m = 456 x 7 = 3192 taka So, 3192 taka be spent for planting grass. Question no : 03 There are two crosswise roads of breadth 3 metres just in the middle of a field of length 50 metres and breadth 40 metres. a. Draw the figure with short description. b. Determine the sum of the area of the two roads. c. How many bricks of construct the two roads with a bricks of length 25 centimetres and breadth 10 centimetres. Solution: (a) A geometric figure based on the given information in the stem is drawn below :

(b) According to the figure drawn in (a) above, Area of the two roads = area of the rectangular region ABCD + area of the rectangular region PQRS + area of the rectangular region KLMN. = 50 × 3 sq. m + 08.5 × 3 sq. m + 18.5 × 3 sq. m = 150 sq. m + 55.5 sq. m + 55.5 sq. m = 261 sq. m The sum of the area of the two roads is 261 sq. m. (c) From (b) above, the total area of two roads = 261 sq. m The area of a brick = 25 x 10 sq. cm = 250 sq. cm = 0.025 sq. m ∴Number of bricks required for constructing the two roads = = 10,440 So, 10,440 piece of bricks are required. Question no : 04 The length of a rectangular plot is 90 meters and breadth is 70 meters. A pond was excavated in this plot with equal bank of width 4 metres around the plot. The depth of the pond is 2.5 meters. a. Find the perimeter of the plot. b. Determine the area of the bank of the pond. c. To dig the soil of the pond, it costs Tk 25 per cubic feet. How much money was spent to dig the soil of the pond? Solution: (a) The length and the breadth of a rectangular plot are 90 m and 70 m respectively. we know, perimeter of a rectangular region = 2(length + breadth) unit ∴The perimeter of the rectangular plot = 2(90+70) m = 2 x 160m = 320 m So, the required perimeter is 320 m. (b)

Here given that, length of the plot with pond and bank = 90 m breadth ” ” ” ” ” ” ” = 70 m area of the plot with pond and bank = 90 x 70 sq m = 6300 sq m Again, length of plot with pond only = (90 – 4×2)m = 82m breadth ” ” ” ” ” = (70 – 4×2)m = 62 m ∴area of plot with pond only = 82 x 62 sq. m = 5084 sq. m So, area of the bank = area of the plot with pond and bank area of the plot with pond only = 6300 sq. m – 5084 sq. m. = 1216 sq. m (c) Here we have, length of the pond = (90 – 4 x 2) m or, 82 m breadth ” ” ” = (70 – 4 x 2) m or, 62 m depth ” ” ” = 2.5 m ∴the volume of the pond = 82 × 62 × 2.5 cu m = 12,710 cu. m = 12,710 × 35.3 cu. ft = 4,48,663 cu. ft So, to excavate the pond, 4,48,663 cu. ft soilis to be dug. Now, if it costs 25 taka per cubic feet to dig the soil of the pond, total cost which will incur in this account = 4,48,663 × 25 = 1,12,16,575 taka ∴1,12,16,575 taka was spent to dig the soil of the pond. (Ans.) Question no : 05 The length of a rectangular garden is 60 metres and breadth is 40 metres. There is a 3 metres wide road outside around the garden. The road is metalled with bricks with 25 cm length and 12.5 cm breadth and price of each brick is Tk. 8. a. Determine the perimeter of garden. b. Determine the area of the road. c. How much money will be needed to metalise the road with brick? Solution: (a) We know, perimeter of a rectangle = 2(Length + breadth) Here in the case of the given rectangular garden, length = 60 m, breadth = 40 m. ∴Perimeter of the garden = 2(60 + 40) m = 200 m. (b) Given that, the length of the garden (without road) = 60 m the breadth of the garden without road = 40 m

∴ area of the garden 60 x 40 sq. m = 2400 sq, m Again, length of the garden with the road of width of 3 m = (60 + 3 + 3) m or 66 m breadth of the garden with road of with 3 m = (40 +3 + 3) m = 46 m ∴ area of the garden with 3 m wide road = 66 x 46 sq. m = 3036 sq. m ∴ area of the road = (3036 – 2400)sq. m = 636 sq. m So, the road is of area of 636 sq. m. (c) From (b) above, the area of the road = 636 sq. m = 6360000 sq. cm Again, the length of a brick =25 cm and the breadth of the brick =12.5 cm ∴area of a brick = 25 x 12.5 sq. cm = 312.5 sq. cm ∴the number of bricks required to cover 6360000 sq. cm road = = 20352 the price of a brick = 8 taka ∴the price of 20352 bricks = 20352 × 8 taka = 162816 taka So, to metalise the road with bricks 162816 taka will be needed. Question no : 06 The length of a rectangular field is 3 times its breadth. An amount of Tk. 1822.50 is spent to plant grass at Tk. 7.50 per sq. meters of that field. a. If the breadth of field be x metre, find the area of the field. b. Find the length and breadth of the rectangular field. c. How many rocks of each 25 cm with sq. size rocks will be needed to construct a square room of which perimeter is equal to the perimeter of the rectangular field? Solution: (a) Let the breadth of the field = x metre ∴Length of the field = 3x metre So, area of the field = 3x × x sq. m = 3x² sq. m (b) Here breadth = x m ∴ length = 3x m ∴area of the rectangular field = 3x × x sq. m = 3x2 sq. m Again, total cost = 1822.50 taka Cost per sq. m = 7.50 taka ∴Total area = sq. m = 243 sq. m ∴3x² = 243 ⇒ x² = 81 ⇒ x = 9. That is, the breadth of the rectangular field is 9 m The length of the field = 3 × 9 m = 27 m (c) From (b), The length of the field = 27 m and the breadth of the field = 9 m. ∴ perimeter of the rectangular field = 2 (27 + 9) = 72 m. ∴ perimeter of the square room = 72 m. ∴ the length of 1 side of the square room=(72 4) m = 18m ∴ the area of the square room = 18 × 18 sq. m = 324 sq. m Again, area of the rock each of 25 cm with sq size = 25 × 25 sq. cm = 625 sq. cm = 0.0625 sq. m Now we have, area of the square room = 324 sq. m and area of each of square rock = 0.0625 sq. m ∴Number of sq rock = pieces = 5184 pieces. So, 5184 pieces of sq rock will be needed to construct the square room. Question no : 07 The area of a rectangular field is 100 acres and its length is three times the breadth. a. Find the area of the rectangular field in sq, metre. b. Find the length of the rectangular field. c. Find the area of a square field which perimeter is same to the rectangular field. Solution: (a) We know, 1 acre = 4046.86 sq. m ∴100 acre = 4046.86 × 100 sq. m = 404686 sq. m ∴the area of the rectangular field is 404686 sq. m. (b) Let the breadth of the rectangular field = x m ∴its length = 3xm ∴its area = 3x × x sq. m. Now according to the problem, 3x² = 404686 or, x² = 134895.33 or, x = 367.28, the breadth of the field ∴3x = 1101.84 That is, the length of the rectangular field is 1101.84 metre. (c) From (b), length of the rectangular field = 1101.84 m breadth of the rectangular field = 367.28 m ∴perimeter of the rectangular field = 2( 1101.84 + 367.28) m = 2938.24 m Now according to the problem, the perimeter of the square field = 2938.24 m ∴ the length of each side of the square = 734.56 rn ∴ area of the square field = 539578.37 sq. m Therefore, the desired area of the square field is 539578.39 sq. m. Question no : 08 The length of a rectangular tank is 5.5 metres and breadth is 4 metres. Breadth is 2 times of the height. It's four sides walls are mettelated with stones having size 1.5 x 1.5 m2. a. Find out the area of the base of the tank. b. What is the volume of water in litre if the tank is full of water and what is the weight of it in kilogram? c. How many stones are needed to mettelated to four sides walls of the tank? Solution: (a) Here the length of the base of a rectangular tank = 5.5 m the breadth of the base of the rectangular tank 4 m ∴ area of the base of the tank = 5.5 × 4 sq. m = 22.0 sq. m So, the desirous area of the base of the tank is 22 sq. m. (b) From (a), area of the base of the tank = 22 sq m height of the tank = × breadth = 2 m ∴ Volume of the tank = 22 × 2 cu. m = 44 cu. m = 44 × 1000000 cu. cm = 44000000 cu. cm Now if the tank is-full of water, the volume of water = 44000000 cu cm = litre = 44000 litre = 44000 kg, since the weight of 1litre of water = 1 kg Therefore, the volume of water of the tank is 44000 litre and its weight is 44000 kg. (c) Here the length, breadth of the base and height of the rectangular tank are 5.5 m, 4 m and 2 m from (a) and (b). ∴area of the 4 side /faces other than the base and the top of the tank = 2(5.5 × 2 + 4 × 2 ) sq. m = 2(11.0 + 8) sq. m =2(19) sq. m = 38 sq. m Again, area of a stone = 1.5 x 1.5 sq. m = 2.25 sq. m So, total area of 4 sides / faces is 38 sq. m and area of a stone is 2.25 sq. m ∴ number of stone = = 16.89 or 17 (approx) Therefore, stones needed to metal the four side wall of the tank is 17 pieces. Question no : 09

In figure, ABCD is a rectangular field, length of which is twice of it's breadth. The total cost of planting grass in the field is Tk. 12160 at the rate of Tk. 3.80 per sq. metre. a. Find the area of the field. b. Find the length of the diagonal AC? c. How much money will be spent at Tk. 7.25 per meter to erect a fence around that field? Solution: (a) Here total cost of planting grass = 12160 taka. Rate of cost of planting grass = 3.80 per sq. m. ∴Area of the field = sq. m = 3200 sq. m. (b) Let the breadth of the rectangular field be x metre. ∴The length of the rectangular field is 2x metre. ∴ its area = 2x × x sq. m = 2x² sq. m But from (a), area = 3200 sq, m. So, 2x² = 3200 or, x² = 1600 or, x = 40 That is, breadth of the rectangular fill is 40 m. ∴The length of the rectangular field= 40×2m= 80 m Now according to the given figure, △ABC is right triangle and is a half of the rectangle ABCD. ∴ AC² = AB² + BC² Here AB = 40 m and BC = 80 m. ∴ AC² = (40)²+ (80)² = 1600 + 6400 = 8000 ∴ AC = 89.44 that is, the length of AC = 89.44 m. (c) From (b), we get, the length of the field 80 m and the breadth of the field = 40 m ∴perimeter of the rectangular field = 2(80 + 40) m = 2(120) m = 240m Now the cost for erecting fence around the field with perimeter of 240 m at the rate of 7.25 taka per metre = 240 × 7.25 taka = 1740 taka. ∴1740 taka will be spent for fencing the field. Question no : 10 Mr Nayeem has a rectangular garden of which length is one and half times its breadth and its area is 2400 sq. metres. There is a 3 metres wide path around the outside of the garden. There is planting grass at Tk. 3.25 per sq. meter of the path. a. In view of the above stem, draw a proportional figure of the rectangular garden with path. b. Find the length and breadth of the garden. c. How much money will be spent in total to the planting grass of the path? Solution: (a) Based on the given information, a proportional figure of the rectangular garden is drawn below :

A rectangular garden ABCD with 3 m path outside around. (b) Let us suppose, the breadth of the garden = x m ∴according to the condition of the problem, the length of the garden = 1.5x m or x m. ∴ area of the garden = x × x sq. m But according to the problem, area of the garden = 2400 sq. m ∴ = 2400 ⇒ 3x² = 2 × 2400 ⇒ x² = ⇒ x² = 1600 ⇒ x = 40 That is the breadth of the garden is 40 m. ∴The length of the garden = x m = = 60 m So, the length is 60 m and the breadth is 40 m of the garden. (c) According to the geometric figure drawn in (a) based on the stem,. area of the garden with 3 m path around outside = (60 +3 + 3) (40 +3 + 3) sq. m = 66 x 46 sq. m = 3036 sq. m Again, area of the garden = 2400 sq. m (given) ∴area of the path = (3036 - 2400) sq, m = 636 sq. m Now amount of money which will be required for planting grass in the path of 636 sq m at the rate of 3.25 taka per sq. m = 636 x 3.25 taka = 2067 taka So, total amount will be spent for planting grass in the path is 2067 taka. Question no : 11 The breadth of a rectangular field is half of its length. An amount of Tk. 12100 is spent to plant grass in the field at the rate of Tk. 2 per sq. metre. Around inside the field there is a road of breadth 4 metres. a. What is the area of the rectangular field. in square metre? b. The expenditure per square metre along the length is Tk. 15 and that of along the breadth is Tk. 10. How much money will be spent to erect a fence around that field? c. How much money will be spent to plant grass in the road at Tk. 12.50 per square metre ? Solution: (a) Here total cost of planting grass = 12100 taka the cost of planting grass per sq. m = 2 taka ∴area of the rectangular field = sq. m = 6050 sq. m. So, the required area of the field is 6050 sq. m. (b) Let the length of the rectangular field = 2x m ∴the breadth of the rectangular field = x m ∴area of the rectangular field = 2x × x sq. m = 2x2 sq. m. But according to (a) above, area is 6050 sq. Read the full article