Question 409315
The perimeter of a rectangle is 240 inches. The length of the rectangle is 4 times the width. Find the dimensions of the rectangle.

As geometry generally says, the formula for the perimeter of a rectangle is:
{{{P = 2l + 2w}}}

Since the length of the rectangle is 4 times the width, we say
{{{l = 4w}}}

Now, by substitution of the given data, we get
{{{240 = 2(4w) + 2w}}} Notice that the length is replaced with 4w as a result of the equation above.
{{{240 = 8w + 2w}}} Multiplication (2 x 4w = 8w).
{{{240 = 10w}}} Addition (8w + 2w = 10).
{{{240/10 = 10w/10}}} Division on both sides.
{{{w = 24}}} Result. (240/10 = 24)

***Since we now have the value of w (width), all we need to do is substitute it to the formula l = 4w (above).

{{{l = 4w}}}
{{{l = 4(24)}}}
{{{l = 96}}}

==================
The dimension are:
length = 96
width = 24
==================

CHECK:
{{{P = 2l + 2w}}}
{{{240 = 2(96) + 2(24)}}}
{{{240 = 192 + 48}}}
{{{240 = 240}}}