The shorter leg of a right triangle is 7m shorter than the longer leg. the hypotenuse is 7m longer than the longer leg. find the side lengths of the triangle.

--------------------------------------------
Define x :
--------------------------------------------
Let the shorter leg = x
Longer leg = x + 7
Hypotenuse = x + 7 + 7 = x + 14 

--------------------------------------------
Solve x :
--------------------------------------------
a² + b² = c²
x² + (x+7)² = (x+14)²
x² + x² + 14x + 49 = x² + 28x + 196
2x² + 14x + 49 = x² + 28x + 196
x² - 14x - 147 = 0
(x - 21)(x + 7) = 0
x = 21 or x = - 7 (rejected, because length cannot be negative)

--------------------------------------------
Find the legs and hypotenuse:
--------------------------------------------
shorter leg = x = 21
longer leg = x + 7 = 21 + 7 = 28
hypotenuse = x + 14 = 21 + 14 = 35

----------------------------------------------------------------------------------------
Answer: The side length of the triangles are 21m, 28, and 35m.
----------------------------------------------------------------------------------------