Question

The Gilberts are you designing a rectangular patio for their backyard. The patio has an area of 432 square feet. The width of the patio is 3/4 its length. What is the length of the patio?

A: 15 feet
B: 24 feet
C: 36 feet
D: 270 feet

Answer 1

B 24ft
X length
Width is 3/4x
X times 3/4x =432

Answer 2

Answer: B: 24 feet.

Explanation:

Let's assume that the length of the rectangular patio is "L" feet. Then, the width of the patio would be 3/4 L.

The area of a rectangle is given by the formula A = L x W, where A is the area, L is the length, and W is the width. We know that the area of the patio is 432 square feet. Substituting the values of L and W, we get:

432 = L x (3/4 L)

Multiplying both sides by 4/3, we get:

(4/3) x 432 = L^2

Simplifying, we get:

576 = L^2

Taking the square root of both sides, we get:

L = ±24

Since the length cannot be negative, the length of the patio is 24 feet.

Therefore, the correct answer is option B: 24 feet.