Question

A rectangle has a length of 20 inches. if its perimeter is 64 inches, what is the area?​

Answer 1

Answer:

$\boxed{ \bold{ \huge{ \boxed{ \sf 240 \: {inches}^{2} }}}}$

Step-by-step explanation:

Given,

Length of a rectangle = 20 inches

Perimeter of a rectangle = 64 inches

Area of a rectangle = ?

Let width of a rectangle be ' w ' .

First, finding the width of a rectangle

$\boxed{ \sf{perimeter = 2(l + w)}}$

plug the values

⇒$\sf{64 = 2(20 + w)}$

Distribute 2 through the parentheses

⇒$\sf{64 = 40 + 2w}$

Swap the sides of the equation

⇒$\sf{40 + 2w = 64}$

Move 2w to right hand side and change it's sign

⇒$\sf{2w = 64 - 40}$

Subtract 40 from 64

⇒$\sf{2w = 24}$

Divide both sides of the equation by 2

⇒$\sf{ \frac{2w}{2} = \frac{24}{2} }$

Calculate

⇒$\sf{w = 12 \: inches}$

Width of a rectangle ( w ) = 12 inches

Now, finding the area of a rectangle having length of 20 inches and width of 12 inches

$\boxed{ \sf{area \: of \: rectangle = length \: \times \: \: width}}$

plug the values

⇒$\sf{area \: of \: rectangle =20 \times 12 }$

Multiply the numbers : 20 and 12

⇒$\sf{area \: of \: rectangle = 240 \: {inches}^{2} }$

Hence, Area of a rectangle = 240 inches²

Hope I helped !

Best regards!