Question

The Gilberts are designing a rectangular patio. The patio has an area of 432 square feet. The width of the patio is its length. What is the length of the patio

Answer 1

The length of the patio is 29.4 feet, calculated by solving the equation derived from the area of a rectangle where the width is half of the length.

Step-by-step explanation:

The Gilberts want to find the length of their rectangular patio, which has an area of 432 square feet and a width that is ½ its length. To solve this, let's use the formula for the area of a rectangle, which is Area = length × width. Let's denote the length as L and the width as W. According to the problem, we know that W = ½L. We then set up the equation 432 = L × (½L). To find L, we solve for L2 = 432 × 2, which gives us L2 = 864. Taking the square root of both sides, we get L = √864, so the length L is 29.4 feet.

Answer 2

Missing info: The width of the patio is 3/4 its length.

Given:
Area = 432 square feet.
length = x
width = 3/4 * x

Area of a rectangle = Length * width
432 ft² = x * 3/4 * x
432 ft²/3/4 = x²
432 ft² * 4/3 = x²
576 = x²
√576 = √x²
24 = x

Length is 24 ft.

Width = 3/4 * 24ft
Width = (3*24)/4
Width = 72/4
Width = 18 ft.