SOLUTION: One leg of a right triangle is 2 m longer than the other leg. The length of the hypotenuse is 10 m.Find the lenght of each side.

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x^2+(x+2)^2=10^2
x^2+x^2+4x+4=100
2x^2+4x+4-100=0
2x^2+4x-96=0
2(x^2+2x+48)=0
2(x+8)(x-6)=0
x-6=0
x=6 m. for the shorter side.
6+2=8 m. for the longer side.
Proof:
6^2+8^2=10^2
36+64=100
100=100

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Let x = the shorter leg.
Then x+2 = the longer leg.
Therefore, by the Pythagorean Theorem:

Now we just solve this. This is a quadratic equation (because of the terms so we will simplify:


... get one side equal to zero ...

... factor ...


... use the Zero Product Property to find what values make the product zero ...
or
Solving these is simple:
or
Since x represents the shorter leg we must reject x = -8 because we don't have negative lengths for legs. So the only acceptable length for the shorter leg is 6. And this makes the longer leg 8 (because it is 2 meters longer).

In summary, the sides of the triangle are 6, 8 and 10 meters long.