# Solve Length of a Rectangle

• Apr 14th 2007, 05:37 AM
thecapaccino
Solve Length of a Rectangle
The length of a rectangle is 5 feet more than the width. The area of the rectangle is 24 square feet. How long is the rectangle?

Now I know it is 8feet long and 3 feet wide...but when I do the following I come out with the wrong answer. Where are am going wrong.

area= length * width
24= length * (width +5)

• Apr 14th 2007, 05:42 AM
topsquark
Quote:

Originally Posted by thecapaccino
The length of a rectangle is 5 feet more than the width. The area of the rectangle is 24 square feet. How long is the rectangle?

Now I know it is 8feet long and 3 feet wide...but when I do the following I come out with the wrong answer. Where are am going wrong.

area= length * width
24= length * (width +5)

Call the width of the rectangle w. The the length, l = w + 5.
A = l*w

24 = (w + 5)w

24 = w^2 + 5w

w^2 + 5w - 24 = 0

(w - 3)(w + 8) = 0

Thus w = 3 or w = -8. But we can't have a negative width, so the width must be w = 3 ft.

Thus l = 3 ft + 5 ft = 8 ft.

-Dan