A sand volleyball court has an area of 144 square meters. Its perimeter is 50 meters. What are the dimensions of the volleyball court?
To find the dimensions of the sand volleyball court, we need to solve a system of equations using the given information.
Let's assume the length of the volleyball court is L meters and the width is W meters.
We have two pieces of information:
1) The area of the court is 144 square meters, so we can write an equation: L * W = 144.
2) The perimeter of the court is 50 meters, which can be expressed as: 2L + 2W = 50.
Now, we can solve this system of equations.
First, rearrange the second equation to solve for L in terms of W:
2L + 2W = 50
2L = 50 - 2W
L = (50 - 2W) / 2
L = 25 - W
Substitute this expression for L into the first equation:
L * W = 144
(25 - W) * W = 144
25W - W^2 = 144
Rearrange this quadratic equation:
W^2 - 25W + 144 = 0
Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. In this case, the equation factors nicely as:
(W - 9)(W - 16) = 0
So, we get two possible solutions for W:
W = 9 or W = 16
Now, substitute these two values of W back into the equation for L:
If W = 9:
L = 25 - W
L = 25 - 9
L = 16
If W = 16:
L = 25 - W
L = 25 - 16
L = 9
Therefore, the dimensions of the sand volleyball court can be either 16 meters by 9 meters or 9 meters by 16 meters.
To find the dimensions of the sand volleyball court, we first need to understand that the court is in the shape of a rectangle. Let's assume the length of the court is 'L' meters and the width is 'W' meters.
The formula to find the area of a rectangle is A = L × W, where A represents the area. In this case, we know that the area is 144 square meters, so we have the equation:
144 = L × W
Next, we know that the perimeter of a rectangle is given by the formula P = 2L + 2W, where P represents the perimeter. In this case, we know that the perimeter is 50 meters, so we have the equation:
50 = 2L + 2W
We have two equations:
1) 144 = L × W
2) 50 = 2L + 2W
We can solve this system of equations to find the values of L and W.
To do that, we can rearrange equation 2) to solve for L:
50 - 2W = 2L
Divide both sides by 2:
25 - W = L
Now, we substitute this value of L in equation 1), we get:
144 = (25 - W) × W
Expanding the equation:
144 = 25W - W^2
Rearranging the equation:
W^2 - 25W + 144 = 0
Now, we can solve this quadratic equation to find the possible values of W.
Using factoring or quadratic formula, we find that the possible values of W are 9 and 16.
If W = 9, then L = 25 - W = 25 - 9 = 16
If W = 16, then L = 25 - W = 25 - 16 = 9
So, the dimensions of the volleyball court could be 16 meters by 9 meters or 9 meters by 16 meters.
x y = 144 so y = 144/x
2x + 2y = 50
2x +2 (144/x) = 50
2 x^2 -50 x + 2*144 = 0
x^2 -25 x + 144 = 0
(x-9) (x-16) = 0
9 by 16
If the dimensions are x and y, then
x+y = 25
xy = 144
x(25-x) = 144
x^2-25x+144 = 0
x = 9,16
So the court is 9x16