Question 1055409
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Find the length of the shorter leg of a right triangle if the longer leg is 8 feet more than the shorter leg 
and the hypotenuse is 8 feet less than twice the shorter leg
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Let x = the length (in ft) of the shorter leg of a right triangle.
Then the longer leg is (x+8) feet.
The hypotenuse is 2x-8.

The Pythagorean theorem says

x^2 + (x+8)^2 = (2x-8)^2.

Simplify and solve for x:

{{{x^2 + x^2 + 16x + 64}}} = {{{4x^2 - 32x + 64}}},

2x^2 - 48x = 0,

x^2 - 24x = 0,

x(x-24) = 0.

The shorter leg is 24 ft. The longer leg is 32 ft. The hypotenuse is 2*24-8 = 40 ft.

And the check is 24^2 + 32^2 = 40^2.

It is (3,4,5)-right-angled triangle.
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