# Areas Quiz Set 004

### Question 1

What is the ratio of the perimeter of a circle of radius 30 units to that of a square having the circle's diameter as its side?

A

π : 4.

B

π : 2.

C

30 : 3.

D

30 : 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 2

The diagonal and one side of a rectangle are 10 m and 8 m. What is the perimeter of the rectangle?

A

28 m.

B

30 m.

C

26 m.

D

32 m.

Soln.
Ans: a

The side = \$√{10^2 - 8^2}\$ = \$√{100 - 64}\$ = 6. So the perimeter = 2 × (8 + 6) = 28 m.

### Question 3

The length and breadth of a rectangular area are in the ratio 9 : 2. What is the length of the field if a car travelling at 10 km/h covers one round of the rectangle in 132 minutes?

A

9 km.

B

11 km.

C

7 km.

D

13 km.

Soln.
Ans: a

Let L = 9x and B = 2x. Perimeter = 2 × (9x + 2x) = speed × time = (10 × 132)/60 = 22 km. So x = 1, and L = 9x = 9 km.

### Question 4

The length and breadth of a rectangle are in the ratio 13 : 2. What is the perimeter if the area is 104 sq. meters?

A

60 meters.

B

62 meters.

C

58 meters.

D

64 meters.

Soln.
Ans: a

Let L = 13x and B = 2x. We are given (13x × 2x) = 104, which gives x = 2. So perimeter = 2 × ((13 × 2) + (2 × 2)) × = 60 meters.

### Question 5

The length and breadth of a rectangle are in the ratio 13 : 7. What is the area if the perimeter is 200 meters?

A

2275 sq. meters.

B

2277 sq. meters.

C

2273 sq. meters.

D

2279 sq. meters.

Soln.
Ans: a

Let L = 13x and B = 7x. We are given 2 × (13x + 7x) = 200, which gives x = 5. So area = L × B = (13 × 5) × (7 × 5) = 2275 sq. meters. 