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

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• Oct 7th 2009, 02:08 AM
sri340
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 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 AM
earboth
Quote:

Originally Posted by sri340
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?

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 $2a^2$

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