Question 354679
Hi,
let x be the length of the hypotenuse.
then the sides are (32 - x) and (x-1)
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Applying the  Pythagorean Theorem*
{{{a^2 + b^2 =c^2}}} where c is the hypotenuse
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{{{(32-x)^2 + (x+1)^2 = x^2}}}
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grinding out and simplifying, we get
{{{x^2 - 66x + 1025 = 0}}}
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Using the quadratic formula 
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
we get
x = 41 Cannot use
or x = 25
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Sides are 7 and 24
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check yur answer
{{{7^2 + 24^2 = 25^2}}}