Question

7) Molly is replacing the rectangular window panes in her house. She will need to order the correct size of glass for each window. Each window will need to be 2 x squared plus 5 x minus 12 inches2. She knows that the width will be x+4 inches. What should the length of the glass pane be?

Answer 1

`x-(1)/(2)`

Explanation:

The area of the rectangular window is equal to the product between the length of the window and its width:

`A=L\cdot W` (1)

where

A is the area

L is the length

W is the width

In this problem, the area of the glass window is

`A=2x^2+5x-12`

This can be rewritten as

`A=(x+4)(x-(1)/(2))` (2)

The two expressions, in fact, are equivalent.

Also, we know that the width is

`W=x+4` (3)

By comparing (1) with (2) and (3), we notice immediately that

`L=x-(1)/(2)`

Therefore, this is the length of the glass pane.