Question 231199
Let x = the shorter leg.
Then x+2 = the longer leg.
Therefore, by the Pythagorean Theorem:
{{{(x)^2 + (x+2)^2 = (10)^2}}}
Now we just solve this. This is a quadratic equation (because of the {{{x^2}}} terms so we will simplify:
{{{x^2 + x^2 + 4x + 4 = 100}}}
{{{2x^2 + 4x + 4 = 100}}}
... get one side equal to zero ...
{{{2x^2 + 4x - 96 = 0}}}
... factor ...
{{{2(x^2 + 2x - 48) = 0}}}
{{{2(x + 8)(x-6) = 0}}}
... use the Zero Product Property to find what values make the product zero ...
{{{x+8 = 0}}} or {{{x-6 = 0}}}
Solving these is simple:
{{{x = -8}}} or {{{x = 6}}}
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).<br>
In summary, the sides of the triangle are 6, 8 and 10 meters long.