# Rectangles

• Jun 24th 2010, 12:02 PM
Veronica1999
Rectangles
Instead of walking along two sides of a rectangular field, Fran took a shortcut along the diagonal, thus saving distance equal to half the length of the longer side. Find the length of the long side of the field, given that the length of the short side is 156 meters.

I tried X + 156 - { ( X+156 )(X+156) +YY} = x/2.
square root the underlined part
I can't do anything with this equation.
• Jun 24th 2010, 12:08 PM
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Quote:

Originally Posted by Veronica1999
Instead of walking along two sides of a rectangular field, Fran took a shortcut along the diagonal, thus saving distance equal to half the length of the longer side. Find the length of the long side of the field, given that the length of the short side is 156 meters.

I tried X + 156 - { ( X+156 )(X+156) +YY} = x/2.
square root the underlined part
I can't do anything with this equation.

Let the short side be x and the long side be y.

Then $\displaystyle \displaystyle \sqrt{x^2+y^2}+\frac{y}{2}=x+y$. Plug in x and solve for y.