Question 141336
hyp=2.4

let l=longer leg, s= shorter leg

l=1.7+s

From the Pythagorean Theorem, a^2+b^2=c^2, c=hypotenuse.

{{{s^2+(1.7+s)^2=2.4^2}}}
{{{s^2+1.7^2+3.4s+s^2=2.4^2}}}
{{{2s^2+3.4s+2.89=5.76}}}
{{{2s^2+3.4s-2.87=0}}}
Normally we would continue here by applying the quadratic formula, however I see a factorization to make it easier:
{{{2(-.618843+s)(0.231884+s)=0}}}
The only answer that makes sense (that is, it is positive), is {{{s=.618843}}}.
So, l=1.7+s=1.7+.618843=2.31884.
Now, check:

{{{.618843^2+(.618843+1.7)^2=.382967+5.37703=5.76}}}
and {{{2.4^2=5.76}}}. This completes the problem.