Mensuration : Quiz

1. If the diagonal of a square is doubled, how does the area of the square change ?
a. Becomes four fold
b. Becomes three fold
c. Becomes two fold
d. None of these
e. Become five fold

2.  If the base of a rectangle is increased by 10% and the area is unchanged, then the corresponding altitude must be decreased by :
a. 100/11%
b. 10%
c. 11%
d. 100/9%
e. 12 %

3. The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and the breadth is increased by 5 cm, the area of the rectangle is increased by 75 cm2.  Therefore, the length of the rectangle is :
a. 20 cm
b. 30 cm
c. 40 cm
d. 50 cm
e. 60 cm

4. A rectangle has 15 cm as its length and 150 cm2 as its area. Its area is increased to 113 times the original area by increasing only its length of its new perimeter is :
a. 50 cm
b. 60 cm
c. 70 cm
d. 80 cm
e. 90 cm

5. The length of a rectangular room is 4 metres. If it can be partitioned into two equal square rooms, what is the length of each partition in metres?
a. 1
b. 2
c. 4
d. Data inadequate.
e. None of these

6. The length and breadth of a square are increased by 40% and 30% respectively. The area of the resulting rectangle exceeds the area of the square by :
a. 42%
b. 62%
c. 82%
d. None of these
e. 40%

7.A hall 20m long and 15m broad is surrounded by a verandah of uniform width of 2.5m. The cost of flooring the verandah at the rate of Rs.3.50 per sq.metre is :
a. Rs.500
b. Rs.600
c. Rs.700
d. Rs.800
e. Rs. 900

8. If the ratio of the areas of two squares is 9:1, the ratio of their perimeters is :
a. 9:1
b. 3:1
c. 3:4
d. 1:3
e. 1:4

9.The length of a rectangle is increased by 60% . By what percent would the width have to be decreased to maintain the same area ?
a. 75/2%
b. 60%
c. 75%
d. 120%
e. 125%

10. A circular wire of radius 42 cm is cut and bent in the form of a rectangle whose sides are in the ratio of 6:5. The smaller side of the rectangle is :
a. 30 cm
b. 60 cm
c. 72 cm
d. 132 cm
e. 144 cm

1/2*d^2/1/2*2d^2 = 1/4

2. A
3. C
b=x and l= 2x
then (2x-5)(x+)-x*2x= 75
2x^2+5x-25-2x^2 = 75 
length = 40 cm

8. B
circumference = 2*22/7*42 = 264 cm
length of rectangle sides are 6x, 5x. then circumference is 2*(6x+5x) = 264,X= 12

smaller side of rectangle = 5x= 60 cm

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