Question

The area of rectangle ABCD is 10 $c{m}^2$ and that of the shaded region is 20 $c{m}^2$. The breadth of the rectangle PQRS is 5 cm. Find the perimeter of the rectangle PQRS.

• A. 22 cm
• B. 44 cm
• C. 30 cm
• D. 150 cm

Answer 1

The correct option is A 22 cm

Area of PQRS = Area of ABCD + Aea of shaded region
= (10 + 20) cm${}^2$
= 30 cm${}^2$

Area of rectangle PQRS = 30 cm${}^2$
and its breadth = 5 cm

We know that,
Area of a rectangle = Length x breadth

So, Length of PQRS = $\frac{Area}{Breadth}$

= $\frac{30}{5}=6cm$

Perimeter of rectangle PQRS
= 2$\times$(length + breadth)
= 2 x (6+5)
= 2 x 11
= 22 cm

Therefore, perimeter of PQRS is 22 cm.