Exercise :: Area  General Questions
1.  The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is: 

Answer: Option B Explanation:
Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 1600 or x = 160. Length = 480 m and Breadth = 320 m. Area = (480 x 320) m^{2} = 153600 m^{2}. 
2.  An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is: 

Answer: Option D Explanation: 100 cm is read as 102 cm. A_{1} = (100 x 100) cm^{2} and A_{2} (102 x 102) cm^{2}. (A_{2}  A_{1}) = [(102)^{2}  (100)^{2}] = (102 + 100) x (102  100) = 404 cm^{2}.

3.  The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle? 

Answer: Option B Explanation:
2l + 2b = 5b 3b = 2l
Then, Area = 216 cm^{2} l x b = 216
l^{2} = 324 l = 18 cm. 
4.  The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is: 

Answer: Option C Explanation: Let original length = x metres and original breadth = y metres. Original area = (xy) m^{2}.
The difference between the original area = xy and newarea 36/25 xy is = (36/25)xy  xy = xy(36/25  1) = xy(11/25) or (11/25)xy

5.  A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road? 

Answer: Option B Explanation: Area of the park = (60 x 40) m^{2} = 2400 m^{2}. Area of the lawn = 2109 m^{2}. Area of the crossroads = (2400  2109) m^{2} = 291 m^{2}. Let the width of the road be x metres. Then, 60x + 40x  x^{2} = 291 x^{2}  100x + 291 = 0 (x  97)(x  3) = 0 x = 3. 