Question

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

• A. 17 cm
• B. 72 cm
• C. 68 cm
• D. 38 cm

Answer 1

The correct option is B 72 cm

Given: Ratio of area of square ABCD to square PQRS = 4:9
The area of square ABCD is 144 sq cm.
Let the area of square PQRS be x.
Now, the given ratio = $\frac{AreaofsquareABCD}{AreaofsquarePQRS}$
$\Rightarrow \frac{4}{9}=\frac{144}{x}$
$\Rightarrow 4x=144\times 9$
$\Rightarrow x=\frac{1296}{4}$
$\Rightarrow x=324$
$\Rightarrow$ Area of square PQRS = 324
$\Rightarrow$ Side $\times$ Side = 324
$\Rightarrow$ Side $\times$ Side = 18 $\times$ 18
$\Rightarrow$ Side of square PQRS = 18 cm

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