Areas Quiz Set 001

Question 1

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.

Question 2

The length and breadth of a rectangle are in the ratio 13 : 6. What is the area if the perimeter is 266 meters?

A

3822 sq. meters.

B

3824 sq. meters.

C

3820 sq. meters.

D

3826 sq. meters.

Soln.
Ans: a

Let L = 13x and B = 6x. We are given 2 × (13x + 6x) = 266, which gives x = 7. So area = L × B = (13 × 7) × (6 × 7) = 3822 sq. meters.

Question 3

The diagonal and one side of a rectangle are 5 m and 3 m. What is the percentage saving of a man who walks along the diagonal instead of the two sides?

A

\$28{4/7}\$%.

B

\$34{1/2}\$%.

C

\$21{4/9}\$%.

D

\$24{5/9}\$%.

Soln.
Ans: a

The side = \$√{5^2 - 3^2}\$ = \$√{25 - 9}\$ = 4. So the saving = (3 + 4) - 5 = 2 meters. So the %-age saving is \$2/7\$ × 100 = \${200/7}\$, which is same as: \$28{4/7}\$%.

Question 4

What is the cost of plastering, @50 paise per square meter, the walls and floor of a 38 m × 14 m. tank that is 8 meters high?

A

Rs. 682 .

B

Rs. 684 .

C

Rs. 680 .

D

Rs. 686 .

Soln.
Ans: a

The area to be plastered is \$(2 × l × h) + (2 × b × h) + (l × b)\$ = (2 × 38 × 8) + (2 × 14 × 8) + (38 × 14) = 1364 sq. m. The cost = 1364 × 0.50 = Rs. 682.

Question 5

What is the smallest number of square tiles that can be laid fully, without cutting, on a floor 10 m by 64 m?

A

160 .

B

161 .

C

159 .

D

162 .

Soln.
Ans: a

The side of the square tile has to be HCF(10, 64) = 2. Hence, the required number is \${10 × 64}/{2 × 2}\$ = 160.