Answer:
8
Step-by-step explanation:
Let x represent the length of the shortest side. Then (x+7) is the length of the longer side, and (3x-7) is the length of the hypotenuse. The Pythagorean theorem gives the relation ...
(3x -7)² = x² +(x +7)²
9x² -42x +49 = x² +x² +14x +49
7x² -56x = 0 . . . . . . . . . subtract the right side, simplify
7x(x -8) = 0
Values of x that satisfy this equation are x=0 and x=8. We know x=0 is not a viable solution, so ...
the shortest side is 8 units long
