Question

The length of a rectangle is five times its width.

Answer 1

Answer:

$\boxed{ \bold{ \huge{ \boxed{ \sf{125 \: {cm}^{2} }}}}}$

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 '

$\boxed{ \sf{perimeter \: of \: a \: rectangle = 2(l + w)}}$

plug the values

⇒$\sf{60 = 2(5w + w)}$

Distribute 2 through the parentheses

⇒$\sf{60 = 10w + 2w}$

Collect like terms

⇒$\sf{60 = 12w}$

Swap the sides of the equation

⇒$\sf{12w = 60}$

Divide both sides of the equation by 12

⇒$\sf{ \frac{12w}{12} = \frac{60}{12} }$

Calculate

⇒$\sf{w = 5}$ cm

Finding the value of length ( l )

$\sf{length = 5w}$

Substitute the value of w

⇒$\sf{length = 5 \times 5}$

⇒$\sf{length = 25 \: cm}$

Finally, Finding the area of rectangle having length of 25 cm and width of 5 cm

$\boxed{ \sf{area \: of \: a \: rectangle = l \times b}}$

plug the values

⇒$\sf{area \: = \: 25 \times 5}$

Multiply the numbers

⇒$\sf{area \: = \: 125 \: {cm}^{2} }$

Hope I helped!

Best regards!!