Question

Perimeter of a square is 24 cm and length of a rectangle is 8 cm. If the perimeters of the square and the rectangle are equal, then the area (in sq cm) of the rectangle is

Answer 1

perimeter Of square and rectangle are equal.

2(l+b)=24cm

l+b=24/2

8+b=12

b=12-8

b=4cm

area of rectangle=l*b

=8*4

@rea of rectangle=32cm²

hope it helps you...

Answer 2

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The area of the Rectangle is 32 cm².

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

Perimeter of the Square = 24 cm

Length of the Rectangle = 8 cm

Perimeter of the Rectangle = Perimeter of the Square

To Find :

The area of the Square

Solution :

As given in the Question,

★ Perimeter of Square = Perimeter of Rectangle

Perimeter of the Rectangle = 24 cm

★ Equation = $\boxed{\sf{2(x+8)=24}}$

$\sf{\longrightarrow} \:2(x + 8) = 24$

$\sf{\longrightarrow} \:2x + 16 = 24$

$\sf{\longrightarrow} \:2x = 24 - 16$

$\sf{\longrightarrow} \:2x = 8$

$\sf{\longrightarrow} \:x = \dfrac{8}{2}$

$\sf{\longrightarrow} \:x = 4$

The Length and Breadth of the Rectangle is 8 cm and Breadth is 4 cm.

$\rule{300}{1.5}$

As We got the Breadth, we can now find the area of the Rectangle.

★ Area = $\boxed{\sf{Length \times Breadth}}$

$\sf{\longrightarrow} \: 8 \times 4$

$\sf{\longrightarrow} \: 32$

$\therefore$ The area of the Rectangle is 32 cm².