# Areas Quiz Set 009

### Question 1

The length and breadth of a rectangle are in the ratio 15 : 7. What is the area if the perimeter is 352 meters?

A

6720 sq. meters.

B

6722 sq. meters.

C

6718 sq. meters.

D

6724 sq. meters.

Soln.
Ans: a

Let L = 15x and B = 7x. We are given 2 × (15x + 7x) = 352, which gives x = 8. So area = L × B = (15 × 8) × (7 × 8) = 6720 sq. meters.

### Question 2

The length and breadth of a rectangle are respectively increased by 11% and 3%. What is the % increase in the area?

A

\$14{33/100}\$%.

B

\$15{16/33}\$%.

C

\$13{7/102}\$%.

D

\$16{101/102}\$%.

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)\$% = \$(11 + 3 + {11 × 3}/100)\$% = \${1433/100}\$, which is same as: \$14{33/100}\$%

### Question 3

A rectangular wire 22 × 18 is re-aligned into a rectangle 11 × 54. What is the percentage increase in area?

A

50 %.

B

52 %.

C

48 %.

D

54 %.

Soln.
Ans: a

By inspection, the length has been halved, and breadth tripled. The %-age increase is known through shortcut formulas to be 50%. So the increase is 50%.

### Question 4

A gun is fired towards a circular board consisting of two concentric circles of radii 19 and 13 cm. If each bullet is able to hit the board, what is the probability that it will strike the ring, i.e., the area between the inner and outer circles?

A

\${192/361}\$.

B

\${32/61}\$.

C

1/2.

D

\${24/47}\$.

Soln.
Ans: a

The area of the ring is equal to the difference of the areas of the two circles. π(\$19^2 - 13^2\$) = 192π sq. cm. The total area is π × 192 = 361π. The probability of hitting the ring is \${192π}/{361π}\$ = \${192/361}\$.

### Question 5

A rectangular wire 18 × 11 is re-aligned into a rectangle 9 × 33. What is the percentage increase in area?

A

50 %.

B

52 %.

C

48 %.

D

54 %.

Soln.
Ans: a

By inspection, the length has been halved, and breadth tripled. The %-age increase is known through shortcut formulas to be 50%. So the increase is 50%. 