given plane figure is a parallelogram area of parallelogram is equal to into height it is equals to 14 into 7 square centimetre is equal to 98 square centimetre
Answers
Question 1:
Find the area of the rectangle whose dimensions are:
(i) length = 24.5 m, breadth = 18 m
(ii) length = 12.5 m, breadth - 8 dm.
ANSWER:
(i) Length = 24.5 m
Breadth = 18 m
∴ Area of the rectangle = Length × Breadth
= 24.5 m × 18 m
= 441 m2
(ii) Length = 12.5 m
Breadth = 8 dm = (8 × 10) = 80 cm = 0.8 m [since 1 dm = 10 cm and 1 m = 100 cm]
∴ Area of the rectangle = Length × Breadth
= 12.5 m × 0.8 m
= 10 m2
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Question 2:
Find the area of a rectangular plot, one side of which is 48 m and its diagonal is 50 m.
ANSWER:
We know that all the angles of a rectangle are 90° and the diagonal divides the rectangle into two right angled triangles.
So, 48 m will be one side of the triangle and the diagonal, which is 50 m, will be the hypotenuse.
According to the Pythagoras theorem:
(Hypotenuse)2 = (Base)2 + (Perpendicular)2
Perpendicular = (Hypotenuse)2−(Base)2−−−−−−−−−−−−−−−−−−−−√
Perpendicular = (50)2−(48)2−−−−−−−−−−√=2500−2304−−−−−−−−−−√=196−−−√=14 m
∴ Other side of the rectangular plot = 14 m
Length = 48m
Breadth = 14m
∴ Area of the rectangular plot = 48 m × 14 m = 672 m2
Hence, the area of a rectangular plot is 672 m2.
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Question 3:
The sides of a rectangular park are in the ratio 4 : 3. If its area is 1728 m2, find the cost of fencing it at Rs 30 per metre.
ANSWER:
Let the length of the field be 4x m.
Breadth = 3x m
∴ Area of the field = (4x × 3x) m2 = 12x2 m2
But it is given that the area is 1728 m2.
∴ 12x2 = 1728
⇒ x2 = (172812) = 144
⇒ x = 144−−−√ = 12
∴ Length = (4 × 12) m = 48 m
Breadth = (3 × 12) m =36 m
∴ Perimeter of the field = 2(l + b) units
= 2(48 + 36) m = (2 × 84) m = 168 m
∴ Cost of fencing = Rs (168 × 30) = Rs 5040
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Question 4:
The area of a rectangular field is 3584 m2 and its length is 64 m. A boy runs around the field at the rate of 6 km/h. How long will he take to go 5 times around it?
ANSWER:
Area of the rectangular field = 3584 m2
Length of the rectangular field = 64 m
Breadth of the rectangular field = (AreaLength) = (358464) m = 56 m
Perimeter of the rectangular field = 2 (length + breadth)
= 2(64+ 56) m = (2 × 120) m = 240 m
Distance covered by the boy = 5 × Perimeter of the rectangular field
= 5 × 240 = 1200 m
The boy walks at the rate of 6 km/hr.
or
Rate = (6×100060) m/min = 100 m/min.
∴ Required time to cover a distance of 1200 m = (1200100) min = 12 min
Hence, the boy will take 12 minutes to go five times around the field.
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Question 5:
A verandah is 40 m long and 15 m broad. It is to be paved with stones, each measuring 6 dm by 5 dm. Find the number of stones required.
ANSWER:
Given:
Length of the verandah = 40 m = 400 dm [since 1 m = 10 dm ]
Breadth of the verandah = 15 m = 150 dm
∴ Area of the verandah= (400 × 150) dm2 = 60000 dm2
Length of a stone = 6 dm
Breadth of a stone = 5 dm
∴ Area of a stone = (6 × 5) dm2 = 30 dm2
∴ Total number of stones needed to pave the verandah = Area of the verandahArea of each stone
= (6000030) = 2000
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Question 6:
Find the cost of carpeting a room 13 m by 9 m with a carpet of width 75 cm at the rate of Rs 105 per metre.
ANSWER:
Area of the carpet = Area of the room
= (13 m × 9 m) = 117 m2
Now, width of the carpet = 75 cm (given)
= 0.75 m [since 1 m = 100 cm]
Length of the carpet = (Area of the carpetWidth of the carpet) = (1170.75) m = 156 m
Rate of carpeting = Rs 105 per m
∴ Total cost of carpeting = Rs (156 ×105) = Rs 16380
Hence, the total cost of carpeting the room is Rs 16380.
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Question 7:
The cost of carpeting a room 15 m long with a carpet of width 75 cm at Rs 80 per metre is Rs 19200. Find the width of the room.
ANSWER:
Given:
Length of the room = 15 m
Width of the carpet = 75 cm = 0.75 m (since 1 m = 100 cm)
Let the length of the carpet required for carpeting the room be x m.
Cost of the carpet = Rs. 80 per m
∴ Cost of x m carpet = Rs. (80 × x) = Rs. (80x)
Cost of carpeting the room = Rs. 19200
∴ 80x = 19200 ⇒ x = (1920080) = 240
Thus, the length of the carpet required for carpeting the room is 240 m.
Area of the carpet required for carpeting the room = Length of the carpet × Width of the carpet
= ( 240 × 0.75) m2 = 180 m2
Let the width of the room be b m.
Area to be carpeted = 15 m × b m = 15b m2
∴ 15b m2 = 180 m2
⇒ b = (18015) m = 12 m
Hence, the width of the room is 12 m.
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Question 8:
The length and breadth of a rectangular piece of land are in the ratio of 5 : 3. If the total cost of fencing it at Rs 24 per metre is Rs 9600, find its length and breadth.
ANSWER:
Total cost of fencing a rectangular piece = Rs. 9600
Rate of fencing = Rs. 24
∴ Perimeter of the rectangular field = (Total cost of fencingRate of fencing) m = (960024) m = 400 m
Let the length and breadth of the rectangular field be 5x and 3x, respectively.
Perimeter of the rectangular land = 2(5x + 3x) = 16x
But the perimeter of the given field is 400 m.
∴ 16x = 400
x = (40016) = 25
Length of the field = (5 × 25) m = 125 m
Breadth of the field = (3 × 25) m = 75 m