Question

A rectangle has a length of 17 inches less than 7 times its width. If the area of the rectangle is 2204square inches, find the length of the rectangle.

Answer 1

SOLUTION

We are told that the length of the rectangle is 17 inches less than 7 times its width.

Now, let the letter L represent the length and the letter w represent the width of the rectangle.

This statement can be represented algebraically as

$L=7w-17$

So, Area =

$\text{Area = L x w}$

We are also told the Area A of the rectangle = 2204. Now

$\begin{gathered} 2204=L\times w \\ \\ 2204=(7w-17)\times w \end{gathered}$

We have to find the width, then we find the length L

$\begin{gathered} 2204=(7w-17)\times w \\ 2204=7w^2-17w \\ 7w^2-17w-2204=0 \\ \\ \text{Solving the quadratic equation } \\ \\ w=19\text{ or w = -16.57} \end{gathered}$

Since the width cannot be negative, w = 19 inches

The length becomes

$\begin{gathered} L=7w-17 \\ L=7\times19-17 \\ L=133-17 \\ L=116\text{ inches } \end{gathered}$