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Let the length of the shorter leg be L, then the longer leg is L + 14.

By Pythagoras then 262 = L2 + (L + 14)2 = L2 + L2 + 28L + 196 = 2L2 + 28L + 196

676 = 2L2 + 28L + 196 : 2L2 + 28L - 480 = 0 : L2 + 14L - 240 = 0

This can be factored : L2 + 14L - 240 = (L + 24)(L - 10) = 0

As only a positive number answer applies and this is when L - 10 = 0 : L = 10.

The length of the shorter leg is 10 feet.

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โˆ™ 2010-03-22 23:22:25
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Q: The hypotenuse of a right triangle is 26 feet long One leg is 14 feet longer than the other Find the length of the shorter leg?
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