Question 1080023
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Let x and y are the legs (the dimensions of the legs, I mean).


Then you have these to equations

x + y + 50 = 112,    (1)    (perimeter)

{{{sqrt(x^2 + y^2)}}} = 50.        (2)    (hypotenuse; Pythagorean equation)

Or, equivalently,

x + y = 62,          (1')

{{{x^2 + y^2}}} = 2500.       (2')

From equation (1') express y = 62-x and substitute it into equation (2'). You will get

{{{x^2 + (62-x)^2}}} = 2500,

{{{x^2 + 3844 - 124x + x^2}}} = 2500,

{{{2x^2 - 124x + 1344}}} = 0,

{{{x^2 - 62x + 672}}} = 0.

Use quadratic formula and complete the solution on your own.
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