# Areas Quiz Set 006

### Question 1

The length and breadth of a rectangle are in the ratio 14 : 3. What is the area if the perimeter is 102 meters?

A

378 sq. meters.

B

380 sq. meters.

C

376 sq. meters.

D

382 sq. meters.

Soln.
Ans: a

Let L = 14x and B = 3x. We are given 2 × (14x + 3x) = 102, which gives x = 3. So area = L × B = (14 × 3) × (3 × 3) = 378 sq. meters.

### Question 2

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

A

48 sq. m.

B

50 sq. m.

C

46 sq. m.

D

52 sq. m.

Soln.
Ans: a

The side = \$√{10^2 - 8^2}\$ = \$√{100 - 64}\$ = 6. So the area = 8 × 6 = 48 sq. m.

### Question 3

The length and breadth of a rectangular area are in the ratio 3 : 1. What is the length of the field if a car travelling at 20 km/h covers one round of the rectangle in 48 minutes?

A

6 km.

B

8 km.

C

4 km.

D

10 km.

Soln.
Ans: a

Let L = 3x and B = 1x. Perimeter = 2 × (3x + 1x) = speed × time = (20 × 48)/60 = 16 km. So x = 2, and L = 3x = 6 km.

### Question 4

The diagonal and one side of a rectangle are 34 m and 16 m. What is the area of the rectangle?

A

480 sq. m.

B

482 sq. m.

C

478 sq. m.

D

484 sq. m.

Soln.
Ans: a

The side = \$√{34^2 - 16^2}\$ = \$√{1156 - 256}\$ = 30. So the area = 16 × 30 = 480 sq. m.

### Question 5

The length of a square is increased by 1%, what is the % increase in area?

A

2.01%.

B

2%.

C

5%.

D

4.02%.

Soln.
Ans: a

If x% is the increase in length, then area increases by \$(2x + x^2/100)\$%. Putting x = 1, the increase is \$(2 × 1 + 1^2/100)\$% = 2.01% 