Question

The areas of two squares ABCD and PQRS are in the ratio of 4 : 9. If the area of ABCD is 144 sq cm, then find the perimeter of square PQRS.

• A. 70 cm
• B. 78 cm
• C. 72 cm
• D. 76

Answer 1

The correct option is C 72 cm

Given: Ratio of area of square ABCD to square PQRS = 4:9

The area of square ABCD is 144 sq cm.

As 4 units represents 144 = $4\times 36$ sq cm
then 1 unit = 36 sq cm

Hence, 9 units = $9\times 36=324$ sq cm

$\Rightarrow$ Area of square PQRS = 324 sq cm
$\Rightarrow$ Side $\times$ Side = 324 sq cm
$\Rightarrow$ Side $\times$ Side = 18 $\times$ 18
$\Rightarrow$ Side of square PQRS = 18 cm

Now, perimeter of square PQRS
$=4\times side$
$=4\times 18$
$=72cm$