# Thread: Word problem with factoring

1. ## Word problem with factoring

I can't seem to figure out this word problem that involves factoring. Here is the question and what I have so far:

"The side of a square equals the width of a rectangle. The length of the rectangle is 6cm longer than its width. The sum of the areas is 176cm^2. Find the length of the side of the square."

I'm not sure whether there are two separate equations in this equation.

s = side of square
w = width of rectangle
area of square = (w)(length)
w = s

length of rectangle = ( w + 6)
area of rectangle = w(w+6)

I've tried pull all in a single equation which isn't. Any advice on how to solve this?

2. ## Re: Word problem with factoring

There is a square consructed on the (short) side of a rectangle
The area of the square is w*w = w^2.
The area of the rectangle is w*(w + 6) = w^2 + 6w.
The sum of these areas is 176.
(w^2) + (w^2 + 6w) = 176
2w^2 - 6w - 176 = 0
w^2 - 3w - 88 = 0
etc.

3. ## Re: Word problem with factoring

You have the area of a rectangle correct. You also know the area of the square is $w^2$

You are told the sum of their areas is 176cm^2 which is the same as $w^2 + w(w+6)=176$

Simplify, solve and discard and solutions less then 0.

4. ## Re: Word problem with factoring

Thanks for the help. This is what I finished with:

(w+11)(w-8)

8 = the length of the side

5. ## Re: Word problem with factoring

Yep, but don't forget your units: $8\text{ cm}$