SOLUTION: The longer leg of a right triangle is 1 ft longer than the shorter leg. The hypotenuse is 9ft longer than the shorter leg. Find the side lengths of the triangle.

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,


     +  = ,   or


     = 

     = 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.


ANSWER.  The longer leg is 21 ft;  the shorter leg is  21-1 = 20 ft.

         The hypotenuse is x+8 = 29 ft.


CHECK.    +  = 441 + 400 = 841 = .    ! Correct !