# Math Help - A rectangle with a diagonal of length is twice as long as it is wide. What is the ar

1. ## A 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 $x$ is twice as long as it is wide. What is the area of the rectangle in terms of $x$?

2. Originally Posted by sri340
A rectangle with a diagonal of length $x$ is twice as long as it is wide. What is the area of the rectangle in terms of $x$?
Let a denote the width, then 2a denote the length.

Calculate the length of the diagonal using Pythagorean theorem:

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

The area of the rectangle is:

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

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

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