4x^2 + 9xy - y^2 = 8
8x + 9xf'(x) + 9y - 2yf'(x) = 0
f'(x) (2y - 9x) = 8x + 9y
f'(x) = (8x + 9y)/(2y - 9x)
In all geometry problems, drawing a diagram is most helpful.
The half-side lengths are 5 feet and 12 feet.
By the Pythagorean Theorem, the hypothenuse, or side length of the rhombus is therefore
sqrt(5^2+12^2)=sqrt(169)=sqrt(13^2)
= 13 feet.
See diagram below.