Question 1138312
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Let x be the longer leg length (in feet).

Then the shorter leg is (x-1) feet long; the hypotenuse is (x+8) feet long.


According to the Pythagorean theorem,


    {{{x^2}}} + {{{(x-1)^2}}} = {{{(x+8)^2}}},   or


    {{{x^2 + x^2 - 2x + 1}}} = {{{x^2 + 16x + 64}}}

    {{{x^2 - 18x - 63}}} = 0


Factor the quadratic polynomial on the left side

    (x-21)*(x+3) = 0.


Its roots are x= 21 and  x= -3,  but only positive solution is meaningful.


<U>ANSWER</U>.  The longer leg is 21 ft;  the shorter leg is  21-1 = 20 ft.

         The hypotenuse is x+8 = 29 ft.


<U>CHECK</U>.   {{{21^2}}} + {{{20^2}}} = 441 + 400 = 841 = {{{29^2}}}.    ! Correct !
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Solved.