Question 494557
x^2 + (x + 17)^2 = (x + 18)^2 
x^2 + x^2 + 34x + 289 =x^2 + 36x + 324
2x^2 + 34x + 289 = x^2 + 36x + 324
x^2 -2x - 35 = 0
(x -7)(x + 5)
x = 7 meters small side
24 meters = other leg.
25 meters  = hypotenuse
7^2 + 24^2 = 25^2
49 + 576 = 635 
This does check.
Cleomenius.