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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?
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 + 196676 = 2L2 + 28L + 196 : 2L2 + 28L - 480 = 0 : L2 + 14L - 240 = 0This can be factored : L2 + 14L - 240 = (L + 24)(L - 10) = 0As 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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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?
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 + 196676 = 2L2 + 28L + 196 : 2L2 + 28L - 480 = 0 : L2 + 14L - 240 = 0This can be factored : L2 + 14L - 240 = (L + 24)(L - 10) = 0As 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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