If a square of side 8m and a rectangle of length 12m have the same perimeter,

Question

If a square of side 8m and a rectangle of length 12m have the same perimeter, then find the area of the rectangle(in m²)?

Options:

A . 36 m²

B . 72 m²

C . 96 m²

D . 48 m²

Answer: Option D
:
D

Let the side of a square be 'a' and length and breadth of a rectangle be 'l' and 'b' respectively.
Given,
Perimeter of square = Perimeter of rectangle

4a = 2(l +b)

4 $\times$ 8 = 2(12 + b)

32 = 24 + 2b

8 = 2b

Hence b = 4 m

Area of rectangle = l $\times$ b = 12 $\times$ 4 = 48 $m^{2}$

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