Question

The length of a rectangle is five inches more than the width. The perimeter is 50 inches. Find the length and the width.

Answer 1

Let l be the length of the rectangle and w be the width, since the length is five inches more than the width we can set the following equation:

$l=w+5in\text{.}$

Also, the perimeter of the rectangle is 50 inches, therefore:

$2l+2w=50in\text{.}$

Substituting the first equation in the second equation we get:

$2(w+5in)+2w=50in\text{.}$

Solving for w we get:

$\begin{gathered} 2w+10in+2w=50in, \\ 4w=40in, \\ w=10in\text{.} \end{gathered}$

Substituting w=10in in the first equation we get:

$\begin{gathered} l=10in+5in, \\ l=15in\text{.} \end{gathered}$

Answer: The length of the rectangle is 15 inches and the width is 10 inches.