Question 1053258
hypotenuse=x
one side is x-1
the third side is x^2-(x-1)^2, which is sqrt {x^2-(x^2-2x+1)}=sqrt (2x-1).
adding 1 to the third side makes it sqrt(2x-1)+1=(1/3)(x-1)=(1/3)x-(1/3)
sqrt(2x-1)=(1/3)x-(4/3)
square both sides
2x-1=(1/9)x^2-(8/9)x+(16/9)
0=(1/9)x^2-(26/9)x+(25/9)
multiply everything by 9
0=x^2-26x+25
(x-25)(x-1)=0;
x=25, 1, and 1 is impossible
x-1=24
The third side is 7 (7,24,25 triangle) and 7+1 is 1/3 of 24.