Question 23845
If we draw the rectangle with width=50, length=x, diagonal=x+10, we find a right triangle with sides 50 and x, and hypotenuse=x+10.  We then use the Pythagorean Theorem to get (x+10)^2 = 50^2 + x^2, so x^2+20x+100=2500+x^2.
When we subtract x^2 from both sides, we get 20x+100=2500, subtracting 100 gives 20x=2400, dividing by 20 gives x=120ft.  So this is the length.