# Areas Quiz Set 005

### Question 1

The diagonal and one side of a rectangle are 13 m and 5 m. What is the area of the rectangle?

A

60 sq. m.

B

62 sq. m.

C

58 sq. m.

D

64 sq. m.

Soln.
Ans: a

The side = \$√{13^2 - 5^2}\$ = \$√{169 - 25}\$ = 12. So the area = 5 × 12 = 60 sq. m.

### Question 2

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 3

A gun is fired towards a circular board consisting of two concentric circles of radii 12 and 3 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

\${15/16}\$.

B

\${5/7}\$.

C

1/2.

D

\${15/31}\$.

Soln.
Ans: a

The area of the ring is equal to the difference of the areas of the two circles. π(\$12^2 - 3^2\$) = 135π sq. cm. The total area is π × 122 = 144π. The probability of hitting the ring is \${135π}/{144π}\$ = \${15/16}\$.

### Question 4

The diagonal and one side of a rectangle are 5 m and 3 m. What is the perimeter of the rectangle?

A

14 m.

B

16 m.

C

12 m.

D

18 m.

Soln.
Ans: a

The side = \$√{5^2 - 3^2}\$ = \$√{25 - 9}\$ = 4. So the perimeter = 2 × (3 + 4) = 14 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%