Answer: 5;12;13
Step-by-step explanation:
let's call the shortest leg
[tex]x[/tex]
and then the longer leg and the hypotenuse
[tex]2x + 2[/tex]
[tex]2x + 3[/tex]
respectively, and then apply pythagorean theorem to the triangle:
[tex]x^2+(2x+2)^2=(2x+3)^2[/tex] at this point is simple number crunching;
[tex] x^2+4x^2+8x+4=4x^2+12x+9 \\ x^2-4x-5=0 \rightarrow (x-5)(x+1)=0[/tex]
the only valid solution is obviously x=5 since its a length of a segment.
