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.
- 
                        View Hint View Answer Discuss in Forum Area of the carpet = Area of the room Correct Option: DArea 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
- 
                        View Hint View Answer Discuss in Forum 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: Dl1 = 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?
- 
                        View Hint View Answer Discuss in Forum 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: CArea 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?
- 
                        View Hint View Answer Discuss in Forum According to the question, 
 4a = 68 [ where a = side]
 ∴a = 68/4 = 17 cm
 ∴ Required area = a2Correct Option: CAccording to the question, 
 4a = 68 [ where a = side]
 ∴a = 68/4 = 17 cm
 ∴ Required area = a2
 = (17)2 = 289 sq cm
-  A railing of 288 m is required for fencing a semi-circular park. Find the area of the park. (π = 22/7)
- 
                        View Hint View Answer Discuss in Forum Let the radius of the park be r, then 
 πr + 2r = 288
 Area of the park = (1/2)πr2Correct Option: ALet the radius of the park be r, then 
 πr + 2r = 288
 (π + 2)r = 288
 ⇒ [(22/7) + 2]r = 288
 ⇒ r = (288 x 7)/36 = 56
 ∴ Area of the park = (1/2)πr2
 = (1/2) x (22/7) x 56 x 56
 = 4928
 
	