# Math - Polygons and Quadrilaterals

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A rectangle has a diagonal of length 125. If the ratio fo the length of the short side to the length of the long side of the rectangle is 7:24, what is the length of the shorter side of the rectangle?

• Math - Polygons and Quadrilaterals -

Recall that the length of a diagonal of a rectangle can be calculated by,
D^2 = W^2 + L^2
or simply, we'll use the Pythagorean theorem.
Substituting,
125^2 = (7x)^2 + (24x)^2
15625 = 49x^2 + 576x^2
15625 = 625x^2
x^2 = 25
x = 5 (this is the multiplier for the ratio)

Therefore, the shorter side (which is 7x) is equal to 7*5 = 35.

Hope this helps~ :3

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