A rectangle with a diagonal of length http://serv.mytjprep.com/brain/mathtex.cgi?x is twice as long as it is wide. What is the area of the rectangle in terms of http://serv.mytjprep.com/brain/mathtex.cgi?x?

- Oct 7th 2009, 02:08 AMsri340A rectangle with a diagonal of length is twice as long as it is wide. What is the ar
A rectangle with a diagonal of length http://serv.mytjprep.com/brain/mathtex.cgi?x is twice as long as it is wide. What is the area of the rectangle in terms of http://serv.mytjprep.com/brain/mathtex.cgi?x?

- Oct 7th 2009, 02:14 AMearboth
Let a denote the width, then 2a denote the length.

Calculate the length of the diagonal using Pythagorean theorem:

$\displaystyle x^2 = (2a)^2+a^2~\implies~x^2 = 5a^2$

The area of the rectangle is:

$\displaystyle A = 2a \cdot a = 2a^2$

Transform the first equation such that the RHS equals $\displaystyle 2a^2$

$\displaystyle x^2 = 5a^2~\implies~\dfrac25 x^2 = 2a^2 = A$