# Areas Quiz Set 009

### Question 1

The diagonal and one side of a rectangle are 17 m and 15 m. What is the percentage saving of a man who walks along the diagonal instead of the two sides?

A

\$26{2/23}\$%.

B

\$28{7/22}\$%.

C

\$23{2/25}\$%.

D

\$26{19/25}\$%.

Soln.
Ans: a

The side = \$√{17^2 - 15^2}\$ = \$√{289 - 225}\$ = 8. So the saving = (15 + 8) - 17 = 6 meters. So the %-age saving is \$6/23\$ × 100 = \${600/23}\$, which is same as: \$26{2/23}\$%.

### Question 2

The length and breadth of a rectangle are in the ratio 19 : 4. What is the perimeter if the area is 304 sq. meters?

A

92 meters.

B

94 meters.

C

90 meters.

D

96 meters.

Soln.
Ans: a

Let L = 19x and B = 4x. We are given (19x × 4x) = 304, which gives x = 2. So perimeter = 2 × ((19 × 2) + (4 × 2)) × = 92 meters.

### Question 3

Three squares have their sides such that they are in an AP(Arithmetic Progression). If the side of the middle square is 8, what is the area of the square whose side is equal to the sum of the sides of these three squares?

A

576 sq. units.

B

580 sq. units.

C

572 sq. units.

D

584 sq. units.

Soln.
Ans: a

Let the sides of the three squares be 8 - d, 8 and 8 + d, where d is the common difference. The sum of these is 24, and the area would be \$24^2\$ = 576 sq. units.

### Question 4

What is the length of the fence required if a square plot of area 1296 sq. m. has to fenced on three sides?

A

108 meters.

B

110 meters.

C

106 meters.

D

112 meters.

Soln.
Ans: a

Area of a square is L2 = 1296, which gives L = 36. If three sides have to be fenced, the required length = 3 × L = 3 × 36 = 108 m.

### Question 5

The diagonal and one side of a rectangle are 10 m and 8 m. What is the area of the rectangle?

A

48 sq. m.

B

50 sq. m.

C

46 sq. m.

D

52 sq. m.

Soln.
Ans: a

The side = \$√{10^2 - 8^2}\$ = \$√{100 - 64}\$ = 6. So the area = 8 × 6 = 48 sq. m.