<PRE><B>Question 655170</B>
    find the length of the short leg of a right triangle if the longer leg is 11 feet more than the shorter leg and the hypotenuse is 11 feet less than twice the shorter leg
.
Let x = length of shorter leg
then
x+11 = longer leg
2x-11 = hypotenuse
.
Applying Pythagorean&#39;s theorem:
x^2 + (x+11)^2 = (2x-11)^2
x^2 + (x+11)(x+11) = (2x-11)(2x-11)
x^2 + (x^2+22x+121) = 4x^2-44x+121
2x^2+22x+121 = 4x^2-44x+121
22x+121 = 2x^2-44x+121
121 = 2x^2-66x+121
0 = 2x^2-66x
0 = 2x(x-33)
x = {0, 33}
throw out the zero (extraneous) leaving
x = 33 feet

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