length = L
width = W
We are told that L = 3W - 10
Area is A
and A = W*L
so 77 = W*(3W-10)
3W^2 - 10W - 77 = 0
(3W + 11)(W - 7) = 0
W = -11/3, W = 7
The width of a rectangle cannot be negative, so ignore the solution W = -11/3.
Then W = 7 and L = 3*7 - 10 = 11
Answer: Width = 7 ft, Length = 11 ft