The perimeter of a rectangular concrete patio is 38 meters. The area is 90 square meters. What are the dimensions of the patio?

2 L + 2 w = 38

so
L + w = 19 and L = 19-w

w L = 90
w (19-w) = 90
w^2 -19 w + 90 = 0
(w-9)(w-10) = 0
9 by 10

Let's assume the length of the rectangular patio is "L" meters and the width is "W" meters.

We know that the perimeter of a rectangle is given by the formula: 2(L + W).

Given that the perimeter is 38 meters, we can write the equation: 2(L + W) = 38.

We also know that the area of a rectangle is given by the formula: L * W.

Given that the area is 90 square meters, we can write the equation: L * W = 90.

Now we have a system of equations:
1) 2(L + W) = 38
2) L * W = 90

We can solve this system of equations to find the dimensions of the patio.

From equation 1, we can isolate L: L = (38 - 2W) / 2.

Substituting this into equation 2:
(38 - 2W) / 2 * W = 90.

Expanding and rearranging the equation:
38W - 2W^2 = 180.

Rearranging again:
2W^2 - 38W + 180 = 0.

We can then solve this quadratic equation for W.

Using the quadratic formula:
W = (-b ± √(b^2 - 4ac)) / (2a).

Plugging in the values: a = 2, b = -38, c = 180.
W = (-(-38) ± √((-38)^2 - 4(2)(180))) / (2(2)).

Simplifying:
W = (38 ± √(1444 - 1440)) / 4.

W = (38 ± √4) / 4.

There are two possible values for W: (38 + 2) / 4 = 10 and (38 - 2) / 4 = 9.

Now that we have the possible values for W, we can substitute them back into the equation L = (38 - 2W) / 2.

For W = 10:
L = (38 - 2(10)) / 2 = 18.

For W = 9:
L = (38 - 2(9)) / 2 = 10.

Therefore, the dimensions of the patio can be either 18 meters by 10 meters or 10 meters by 9 meters.

To find the dimensions of the rectangular patio, we can set up a system of equations using the given information.

Let's assume that the length of the patio is l meters and the width is w meters.

We know that the perimeter of a rectangle is given by the formula:
Perimeter = 2(length + width)

From the given information, we can set up the equation:
38 = 2(l + w)

We also know that the area of a rectangle is given by the formula:
Area = length * width

From the given information, we can set up the equation:
90 = l * w

We now have a system of two equations with two variables. We can solve this system to find the values of l and w.

Let's rearrange the first equation to solve for l:
38 = 2l + 2w
38 - 2w = 2l
l = (38 - 2w) / 2
l = 19 - w

Substitute the value of l in the second equation:
90 = (19 - w) * w
90 = 19w - w^2

Rearrange the equation to solve for w^2:
w^2 - 19w + 90 = 0

We now have a quadratic equation that we need to solve to find the possible values for w. Factoring or using the quadratic formula can help us find the solutions for w. Let's use the quadratic formula:

w = [-(-19) ± √((-19)^2 - 4 * 1 * 90)] / (2 * 1)
w = [19 ± √(361 - 360)] / 2
w = [19 ± √1] / 2

w = (19 + 1) / 2 or w = (19 - 1) / 2
w = 20 / 2 or w = 18 / 2
w = 10 or w = 9

So, we have two possible values for the width, w = 10 meters or w = 9 meters.

Now, substitute these values back into the equation for l:
If w = 10 meters:
l = 19 - 10
l = 9 meters

If w = 9 meters:
l = 19 - 9
l = 10 meters

Therefore, the dimensions of the rectangular patio could be 9 meters by 10 meters or 10 meters by 9 meters.

I dont understand how you got the answer