# Areas Quiz Set 007

### Question 1

The length and breadth of a rectangular area are in the ratio 9 : 7. What is the length of the field if a car travelling at 15 km/h covers one round of the rectangle in 384 minutes?

A

27 km.

B

29 km.

C

25 km.

D

31 km.

Soln.
Ans: a

Let L = 9x and B = 7x. Perimeter = 2 × (9x + 7x) = speed × time = (15 × 384)/60 = 96 km. So x = 3, and L = 9x = 27 km.

### Question 2

The length and breadth of a rectangle are in the ratio 19 : 4. What is the perimeter if the area is 304 sq. meters?

A

92 meters.

B

94 meters.

C

90 meters.

D

96 meters.

Soln.
Ans: a

Let L = 19x and B = 4x. We are given (19x × 4x) = 304, which gives x = 2. So perimeter = 2 × ((19 × 2) + (4 × 2)) × = 92 meters.

### Question 3

What is the ratio of the perimeter of a circle of radius 12 units to that of a square having the circle's diameter as its side?

A

π : 4.

B

π : 2.

C

12 : 3.

D

12 : π.

Soln.
Ans: a

Let X be the radius of the circle, so the side of the square is 2X. The ratio of the perimeters = \${2 × π × X}/{4 × (2X)}\$ = π/4.

### Question 4

What is the length of the fence required if a square plot of area 64 sq. m. has to fenced on three sides?

A

24 meters.

B

26 meters.

C

22 meters.

D

28 meters.

Soln.
Ans: a

Area of a square is L2 = 64, which gives L = 8. If three sides have to be fenced, the required length = 3 × L = 3 × 8 = 24 m.

### Question 5

What is the area of the largest square that can be drawn inside a circle of radius 19 m?

A

722 sq. m.

B

723 sq. m.

C

721 sq. m.

D

724 sq. m.

Soln.
Ans: a

If the radius of the circle is R, then the side of an inscribed square is \$√2 × R\$, so the area is 2 × R2 = 2 × 192 = 722 sq. m. 