# Finding the length of a diagonal

• January 30th 2010, 09:20 AM
fmc123
Finding the length of a diagonal
The width of a rectangle is 1 less than twice its length. If the area of the rectangle is 90 cm^2, what is the length of the diagonal?

I know this has to do with the Pythagorean theorem, however, I just have not been able to figure out the answer. Help?
• January 30th 2010, 09:25 AM
e^(i*pi)
Quote:

Originally Posted by fmc123
The width of a rectangle is 1 less than twice its length. If the area of the rectangle is 90 cm^2, what is the length of the diagonal?

I know this has to do with the Pythagorean theorem, however, I just have not been able to figure out the answer. Help?

$A = \frac{1}{2}ab = 90$

$a = 2b-1$

You can then use Pythagoras.

$d^2 = (2b-1)^2+b^2$