9514 1404 393
Answer:
 15 in, 36 in, 39 in
Step-by-step explanation:
The Pythagorean theorem tells us that for short side x, the relation is ...
 (2x +9)² = (2x +6)² +x²
 4x² +36x +81 = 4x² +24x +36 +x²
 x² -12x -45 = 0 . . . . . subtract the left-side expression
 (x -15)(x +3) = 0 . . . . factor
 x = 15 . . . . . . . . . . . the positive value of x that makes a factor zero
The side lengths of the triangle are 15 inches, 36 inches, and 39 inches.
