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.

Answer 1

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

The area of square ABCD is 144 sq cm.

4 parts in the ratio represents 144 sq cm.
So, 1 part = 144 $÷$ 4 = 36 sq cm

Area of square PQRS = 9 parts = $9\times 36=324$ 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 $=4\times \text{side}$ $=4\times 18$ $=72\text{cm}$