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.