Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{125 \: {cm}^{2} }}}}}[/tex]
Step-by-step explanation:
Let the width be 'w'
Length of a rectangle = 5w
Perimeter of a rectangle = 60 cm
Area of a rectangle = ?
First, finding the value of width ' w '
[tex] \boxed{ \sf{perimeter \: of \: a \: rectangle = 2(l + w)}}[/tex]
plug the values
⇒[tex] \sf{60 = 2(5w + w)}[/tex]
Distribute 2 through the parentheses
⇒[tex] \sf{60 = 10w + 2w}[/tex]
Collect like terms
⇒[tex] \sf{60 = 12w}[/tex]
Swap the sides of the equation
⇒[tex] \sf{12w = 60}[/tex]
Divide both sides of the equation by 12
⇒[tex] \sf{ \frac{12w}{12} = \frac{60}{12} }[/tex]
Calculate
⇒[tex] \sf{w = 5}[/tex] cm
Finding the value of length ( l )
[tex] \sf{length = 5w}[/tex]
Substitute the value of w
⇒[tex] \sf{length = 5 \times 5}[/tex]
⇒[tex] \sf{length = 25 \: cm}[/tex]
Finally, Finding the area of rectangle having length of 25 cm and width of 5 cm
[tex] \boxed{ \sf{area \: of \: a \: rectangle = l \times b}}[/tex]
plug the values
⇒[tex] \sf{area \: = \: 25 \times 5}[/tex]
Multiply the numbers
⇒[tex] \sf{area \: = \: 125 \: {cm}^{2} }[/tex]
Hope I helped!
Best regards!!
