Question

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a rectangle and square have an equal area. if the length and the perimeter of a rectangule is 16 cm 40 cm respectively then find the perimeter and area of the square.

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Answer 1

Answer: Area = 64cm² and perimeter = 32 cm

Step-by-step explanation:

Length of the rectangle = 16 cm

Perimeter of the rectangle = 40 cm

But Perimeter = 2(length+breadth)

So 2(16+breadth)=40

16+breadth=20

breadth=4 cm

Area of the rectangle = length x breadth

= 16x4=64

But given area of the rectangle = area of the square

So area of the square = 64 cm²

side²=64

So side = √64 = 8

Hence perimeter of the square = 4xside

= 4x8

=32 cm

Answer 2

$\textsf{\large{Answer}}$

Area of the square = 64 sq.cm

Perimeter of the square = 32 cm

$\textsf{\large{Explaination:-}}$

First we need to find the Breadth of the Rectangle.

Length of the Rectangle = 16 cm

Perimeter of the Rectangle = 40 cm

$\textbf{Perimeter of Rectangle}$

$\tt{ \Rightarrow 2(b + l)}$

$\tt{ \Rightarrow 2(b + 16) = 40}$

$\tt{ \Rightarrow 2b + 32 = 40}$

$\tt{ \Rightarrow 2b = 40 - 32}$

$\tt{ \Rightarrow b \: = \dfrac{8}{2} }$

$\tt{ \Rightarrow b = 4}$

$\tt{ \Rightarrow 4 \: cm}$

$\textbf{Area of Rectangle}$

$\tt{ \Rightarrow l \times b}$

$\tt{ \Rightarrow 16 \times 4}$

$\tt{ \Rightarrow 64}$

$\tt{ \Rightarrow 64 cm^{2} }$

It is given that the area of the given square = the area of the given Rectangle

$\therefore$The area of the square = 64 cm²

$\textbf{Now area of a square}$

$\tt{ \Rightarrow (side)^{2} }$

$\tt{ \Rightarrow (side)^{2} = 64 }$

$\tt{ \Rightarrow side \: = \sqrt{64} }$

$\tt{ \Rightarrow side \: = 8cm}$

$\therefore$The side of the given square is 8cm

$\textbf{Perimeter of square}$

$\tt{ \Rightarrow side \times 4}$

$\tt{ \Rightarrow 8 \times 4}$

$\tt{ \Rightarrow32cm }$

$\therefore$$\textsf{\large{The Area is 64sq.cm}}$

$\therefore$$\textsf{\large{The Perimeter is 32cm }}$