Answer:
6,8
Step-by-step explanation:
Using Pythagoras's Theorem, we can find out that:
[tex]x^2 + (x+2)^2 = 10^2[/tex]
This simplifies to:
[tex]x^2 + x^2 + 4x +4 = 100[/tex]
[tex]2x^2 + 4x - 96 =0[/tex]
You can simplify this further by dividing by 2:
[tex]x^2 +2x - 48[/tex] = 0
(x+8)(x-6) = 0
x = 6 or x = -8
Since it's a triangle, we can't have negative sides so x = 6.
The shorter leg is 6, the longer leg is 8.
