Question

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

Answer 1

`\boxed{ \bold{ \huge{ \boxed{ \sf 240 \: {inches}^(2) }}}}`

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{ (2w)/(2) = (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 \: * \: \: width}}`

plug the values

⇒
`\sf{area \: of \: rectangle =20 * 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!