Question

Question 53

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.

Answer 1

Let breadth of rectangle = b cm

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

But according to question,

perimeter of Rectangle = Perimeter of square

$\Rightarrow$ 2$\times$(Length + Breadth) = 60

$\Rightarrow$ 2(18 + b) =60

$\Rightarrow$ $\frac{2\times (18+b)}{2}=\frac{60}{2}$ [dividing both sides by 2]

$\Rightarrow$ 18 + b = 30

$\Rightarrow$ b = 30 - 18 [transposing 18 to RHS]

$\Rightarrow$ b = 12

Now, area of rectangle = Length $\times$Breadth

= 18$\times$12

= 216 sq cm