The shorter leg of a right triangle is 7 m shorter than the longer leg. The hypotenuse is 7 m longer than the longer leg. Find the side length of the triangle.
Let x be the length of the longer leg.
Then the shorter leg is x - 7, and the hypotenuse is x + 7.
From the Pythagorean theorem, we have:
(x - 7)^2 + x^2 = (x + 7)^2
Expanding and simplifying:
x^2 - 14x + 49 + x^2 = x^2 + 14x + 49
2x^2 - 28x + 49 = x^2 + 14x + 49
x^2 - 42x = 0
x(x - 42) = 0
x = 0 or x = 42
Since the side length of a triangle can't be zero, x = 42 m is the length of the longer leg.
Therefore, the shorter leg is 42 - 7 = 35 m, and the hypotenuse is 42 + 7 = 49 m.