# Areas Quiz Set 002

### Question 1

The length and breadth of a rectangle are in the ratio 3 : 1. What is the perimeter if the area is 27 sq. meters?

A

24 meters.

B

26 meters.

C

22 meters.

D

28 meters.

Soln.
Ans: a

Let L = 3x and B = 1x. We are given (3x × 1x) = 27, which gives x = 3. So perimeter = 2 × ((3 × 3) + (1 × 3)) × = 24 meters.

### Question 2

What is the area of the largest circle that can fit completely inside a square of side 18 meters?

A

81π sq. m.

B

162π sq. m.

C

6561π sq. m.

D

40.5π sq. m.

Soln.
Ans: a

The radius of such a circle is 18/2 = 9 m. So its area = π × 9 × 9 = 81π sq. m.

### Question 3

Two concentric circles of radii 18 and 16 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

68π sq. cm.

B

136π sq. m.

C

4624π sq. m.

D

34π sq. m.

Soln.
Ans: a

The required area is difference of the areas of the two circles. π(\$18^2 - 16^2\$) = 68π sq. cm.

### Question 4

The length and breadth of a rectangle are respectively increased by 13% and 10%. What is the % increase in the area?

A

\$24{3/10}\$%.

B

\$28{1/9}\$%.

C

\$19{5/12}\$%.

D

\$22{3/4}\$%.

Soln.
Ans: a

If x% and y% is the increase in the dimensions, then the area of a rectangle increases by \$(x + y + {xy}/100)\$% = \$(13 + 10 + {13 × 10}/100)\$% = \${243/10}\$, which is same as: \$24{3/10}\$%

### Question 5

The difference between the length and breadth of a rectangle is 30 m. What is the area if the perimeter is 92 meters?

A

304 sq. meters.

B

306 sq. meters.

C

302 sq. meters.

D

308 sq. meters.

Soln.
Ans: a

If L and B are the length and breadth of the rectangle, then L - B = 30 and 2(L + B) = 92. Solving, we get L = 38 and B = 8, so the area is 38 × 8 = 304 sq. m. TIP: Sometimes long multiplications can be avoided by looking at the units place of the given options. 