Area of a rectangle = A = (width)(length).
Here, the area is 24 ft^2, and this equals ( [3/4]L)(L), where [3/4]L represents the width and L the length.
Then 24 ft^2 = [3/4]L^2.
Multiplying both sides of this equation by 4/3 isolates L^2:
[4/3](24 ft^2) = L^2, or 32 ft^2 = L^2.
Taking the square root of both sides: L = +√(32 ft^2).
The latter result separates as follows: L = +√16*√2, or L = + 4√2.
The length of the patio is 4√2 feet, or approx. 5.66 ft.