Area and Perimeter
- Find the cost of carpeting a room 8 m long and 6 m broad with a carpet 75 cm wide at ₹ 20 per m.
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Area of the carpet = Area of the room
Correct Option: D
Area of the carpet = Area of the room
= 8 x 6 = 48 sq m
Width of the carpet = 75/100 = 3/4 m
Length of the carpet = 48 x (4/3)
= 16 x 4 = 64 m
∴ Cost of carpeting = 64 x 20 = ₹ 1280
- A rectangle has 20 cm as its length and 200 sq cm as its area. If the area is increased by 11/5 time the original area by increase its length only then the perimeter of the rectangle so formed (in cm) is
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l1 = 20 cm, A1 = 200 sq cm
∴ b1 = 200/20 = 10 cm
Now, A2 = 200 x 6/5 = 240 sq cm
b2 = 10 cm
∴ l2 = 240/10 = 24 cm
∴ Perimeter of new rectangle = 2(l2 + b2)Correct Option: D
l1 = 20 cm, A1 = 200 sq cm
∴ b1 = 200/20 = 10 cm
Now, A2 = 200 x 6/5 = 240 sq cm
b2 = 10 cm
∴ l2 = 240/10 = 24 cm
∴ Perimeter of new rectangle = 2(l2 + b2)
= 2(24 + 10) = 2 x 34 = 68 cm
- The breadth of a rectangle is 25 m. The total cost of putting a grass bed on this field was ₹ 12375, at the rate of ₹ 15 per sq m. What is the length of the rectangular field?
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Area to the rectangular field = 12375/15 = 825 sq m
According to the question,
(L x B) = 825 [L = length and B = breadth]Correct Option: C
Area to the rectangular field = 12375/15 = 825 sq m
According to the question,
(L x B) = 825 [L = length and B = breadth]
⇒ L x 25 = 825
∴ L = 825/25 = 33 m
- What is the area of a square having perimeter 68 cm?
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According to the question,
4a = 68 [ where a = side]
∴a = 68/4 = 17 cm
∴ Required area = a2Correct Option: C
According to the question,
4a = 68 [ where a = side]
∴a = 68/4 = 17 cm
∴ Required area = a2
= (17)2 = 289 sq cm
- The perimeter of two squares are 68 cm. Find the perimeter of the third square whose area is equal to the different of the areas of these two squares.
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a1 = 68/4 = 17 cm
and a2 = 60/4 = 15 cm
[ where a1 and a2 are sides]
According to the question,
Area of the third square = [(17)2 - (15)2 ]Correct Option: C
a1 = 68/4 = 17 cm
and a2 = 60/4 = 15 cm
[ where a1 and a2 are sides]
According to the question,
Area of the third square = [(17)2 - (15)2 ]
= (17 + 15) (17 - 15)
= 32 x 2
= 64 sq cm
Let a3 = Side of the third square.
According to the question, (a3)2 = 64 sq cm
∴ a3 = √64 = 8 cm
∴ Perimeter of the third square = 4 x a3 = 4 x 8 = 32 cm.