# Areas Quiz Set 020

### Question 1

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 2

The diagonal and one side of a rectangle are 26 m and 24 m. What is the perimeter of the rectangle?

A

68 m.

B

70 m.

C

66 m.

D

72 m.

Soln.
Ans: a

The side = \$√{26^2 - 24^2}\$ = \$√{676 - 576}\$ = 10. So the perimeter = 2 × (24 + 10) = 68 m.

### Question 3

Two concentric circles of radii 14 and 7 cm are drawn on a paper. What is the area of the portion that is inside the outer circle but outside the inner circle?

A

147π sq. cm.

B

294π sq. m.

C

21609π sq. m.

D

73π sq. m.

Soln.
Ans: a

The required area is difference of the areas of the two circles. π(\$14^2 - 7^2\$) = 147π sq. cm.

### Question 4

The length of a square is increased by 4%, what is the % increase in area?

A

8.16%.

B

17%.

C

11%.

D

16.32%.

Soln.
Ans: a

If x% is the increase in length, then area increases by \$(2x + x^2/100)\$%. Putting x = 4, the increase is \$(2 × 4 + 4^2/100)\$% = 8.16%

### Question 5

The difference between the length and breadth of a rectangle is 2 m. What is the area if the perimeter is 8 meters?

A

3 sq. meters.

B

5 sq. meters.

C

9 sq. meters.

D

7 sq. meters.

Soln.
Ans: a

If L and B are the length and breadth of the rectangle, then L - B = 2 and 2(L + B) = 8. Solving, we get L = 3 and B = 1, so the area is 3 × 1 = 3 sq. m. TIP: Sometimes long multiplications can be avoided by looking at the units place of the given options. 