Question

Perimeter of a square and a rectangle is same. If a side of the square is 15 cm and one side of the rectangle is 18 cm, find the area of the rectangle.
[3 marks]

Answer 1

Given, length of rectangle = 18 cm
and side of square = 15 cm

$\therefore$ Perimeter of a square = 4$\times$Side
= 4$\times$ 15
= 60 cm
[1 mark]
But according to question,
Perimeter of Rectangle = Perimeter of square
Let breadth of rectangle = b cm
⇒ 2$\times$(Length + Breadth) = 60 cm
⇒ 2 (18 cm + b cm) = 60 cm
⇒ $\frac{2\times (18cm+bcm)}{2}=\frac{60cm}{2}$ [dividing both sides by 2]
⇒ 18 cm + b cm = 30 cm
[1 mark]
⇒ b = 30 cm - 18 cm [transposing 18 to RHS]
⇒ b = 12 cm
[0.5 mark]
Now, area of rectangle = Length $\times$Breadth
⇒ 18 cm$\times$ 12 cm = 216 sq cm
[0.5 mark]