The Gilbert's are designing a rectangular patio. The patio has an area of 24 square feet. The width of the patio is 3/4 it's length. What is the length of the patio

5.66 ft

Step-by-step explanation:

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.