A rectangular concrete patio has an area of 360 square meters and a perimeter of 76 meters. What are the dimensions of the patio? meters by meters

Let's denote the length of the patio as L and the width as W.

From the problem, we know two things:

1. The area of the patio is 360 square meters. The formula for the area of a rectangle is A = L * W. So, we have:

360 = L * W ---- (equation 1)

2. The perimeter of the patio is 76 meters. The formula for the perimeter of a rectangle is P = 2L + 2W. So, we have:

76 = 2L + 2W ---- (equation 2)

We can simplify equation 2 by dividing every term by 2, which gives us:

38 = L + W ---- (equation 3)

Now we have a system of two equations, and we can solve it step by step.

First, let's express L from equation 3:

L = 38 - W

Now we can substitute L in equation 1:

360 = (38 - W) * W 360 = 38W - W^2

Rearranging terms gives us a quadratic equation:

W^2 - 38W + 360 = 0

We can solve this quadratic equation to find W. The solutions of the equation are W1 = 20 and W2 = 18.

Substituting W back into equation 3 gives us the corresponding lengths: L1 = 18 and L2 = 20.

So, the dimensions of the patio are 20 meters by 18 meters.