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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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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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Related questions

He length of the longer leg of a right triangle is 3ft more than three times the length of the shorter leg. The length of the hypotenuse is 4ft more than three times the length of the shorter leg. Fin?

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