Question

The Gilbert's are designing a rectangular patio. The patio has an area of 432 square feet. The width of the patio is 3/4 it's length. What is the length of the patio

Answer 1

Represent the unknowns.
Let x = length
since the width is 3/4 of the length,
Let (3/4)x = width

Recall that the area of rectangle is just width multiplied by the length,
A = w * l
Substituting,
432 = (3/4)x * x
432 = (3/4)x^2
432 * 4/3 = x^2
576 = x^2
Get the square root of both sides,
x = 24 feet (length)