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

I really tried it but my teacher was not getting really in dept with this problem. Please help me. Ii have no work to show because I don't even understand the problem.

Length = L ft.

Width = 3L/4

A = L * 3L/4 = 432 Ft^2
Solve for L.

24

To solve this problem, let's break it down step by step:

Step 1: Determine the formula for the area of a rectangle:
Area = length x width

Step 2: Use the given information to form an equation:
We are told that the area of the patio is 432 square feet, and the width is 3/4 of the length. Let's represent the length of the patio as "L" and the width as "W". According to the problem, W = (3/4)L.

Step 3: Substitute the width value into the area formula:
Since we know that the area is 432 square feet and the width is (3/4)L, we can substitute these values into the area formula to get:
432 = L x (3/4)L

Step 4: Solve the equation for L:
To solve this equation, we can start by simplifying it:
432 = (3/4)L x L
432 = (3L^2)/4

Next, multiply both sides of the equation by 4 to eliminate the fraction:
4 x 432 = 3L^2
1728 = 3L^2

Now, divide both sides of the equation by 3 to isolate L^2:
1728/3 = L^2
576 = L^2

Step 5: Take the square root of both sides to solve for L:
√576 = √L^2
24 = L

So, the length of the patio is 24 feet.

To find the length of the rectangular patio, we can follow these steps:

Step 1: Let's assign a variable to the unknown quantity. In this case, let's call the length "L."

Step 2: We are given that the width of the patio is 3/4 of its length. In mathematical terms, this can be expressed as: width = (3/4) * length.

Step 3: Now, we know that the area of a rectangle is given by the formula: area = length * width. Substituting the given values, we get: 432 = L * ((3/4) * L).

Step 4: Simplifying the equation, we can multiply 3/4 with L: 432 = (3/4) * L^2.

Step 5: To remove the fraction, we can multiply both sides of the equation by 4. Doing so, we have: 432 * 4 = 3 * L^2.

Step 6: Simplifying further, we get: 1728 = 3L^2.

Step 7: Divide both sides of the equation by 3 to isolate L^2: (1728 / 3) = L^2.

Step 8: Calculate the value on the left side of the equation: 576 = L^2.

Step 9: Finally, take the square root of both sides to solve for L: √576 = L.

Step 10: Evaluating the square root, we have two possible values: L = ±24.

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

So, the length of the rectangular patio is 24 feet.