Question 1064331
Just one right angle opposite of the 60 foot distance between the two trees;  being hypotenuse of a right triangle, same as half of a rectangle.  Path length wanted, 70 feet.



Let x be one of the leg lengths.  The other leg length is 70-x.

Your equation is correct.
{{{x^2+(70-x)^2=60^2}}}
Simplify and solve.


{{{x^2+70^2-140x+x^2=3600}}}


{{{2x^2-140x+70^2-3600=0}}}


{{{2x^2-140x+4900-3600=0}}}


{{{x^2-70x+650=0}}}
Can the quadratic be factored?

No.
Discriminant  {{{4900-4*650=2300=10^2*23}}}


General Solution Formula for a Quadratic Equation.....
{{{x=(70+- 10*sqrt(23))/(2*2)}}}

{{{x=(35+- 5*sqrt(23))/2}}}


x=5.510  or  x=29.490
You can check if these work in the original {{{x^2+(70-x)^2=60^2}}} equation or not.