Question 1014185
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A garden has the shape of a right triangle with one leg 7 meters longer than the other. The hypotenuse is 7 meters less than twice the length of the shorter leg. What is the length of the shorter leg?
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So, the legs are x and x+7, while the hypotenuse is 2x-7.

The Pythagorean equation is 

{{{x^2 + (x+7)^2}}} = {{{(2x-7)^2}}},   or

{{{x^2 + x^2 + 14x + 49}}} = {{{4x^2 - 28x + 49}}},   or

{{{2x^2 - 42x}}} = {{{0}}}

with the only appropriate solution x = 21.

<U>Check</U>: 21^2 + (21+7)^2 = 21^2 + 28^2 = 1225;
       (2*21 - 7)^2 = 35^2 = 1225.

<U>Answer</U>. The shorter leg is 21 meter.
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