Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf 240 \: {inches}^{2} }}}}[/tex]
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
[tex] \boxed{ \sf{perimeter = 2(l + w)}}[/tex]
plug the values
⇒[tex] \sf{64 = 2(20 + w)}[/tex]
Distribute 2 through the parentheses
⇒[tex] \sf{64 = 40 + 2w}[/tex]
Swap the sides of the equation
⇒[tex] \sf{40 + 2w = 64}[/tex]
Move 2w to right hand side and change it's sign
⇒[tex] \sf{2w = 64 - 40}[/tex]
Subtract 40 from 64
⇒[tex] \sf{2w = 24}[/tex]
Divide both sides of the equation by 2
⇒[tex] \sf{ \frac{2w}{2} = \frac{24}{2} }[/tex]
Calculate
⇒[tex] \sf{w = 12 \: inches}[/tex]
Width of a rectangle ( w ) = 12 inches
Now, finding the area of a rectangle having length of 20 inches and width of 12 inches
[tex] \boxed{ \sf{area \: of \: rectangle = length \: \times \: \: width}}[/tex]
plug the values
⇒[tex] \sf{area \: of \: rectangle =20 \times 12 }[/tex]
Multiply the numbers : 20 and 12
⇒[tex] \sf{area \: of \: rectangle = 240 \: {inches}^{2} }[/tex]
Hence, Area of a rectangle = 240 inches²
Hope I helped !
Best regards!
