The perimeter of a beach volleyball court is 54 m. The difference
between its length and its width is 9 m.
a) Create a linear system to model this situation.
b) Solve the system to determine the dimensions of the court.
Let's denote the length of the beach volleyball court as L and the width as W.
Given that the perimeter is 54 m, we can write the equation for the perimeter as:
2L + 2W = 54
Given that the difference between the length and width is 9 m, we can write the equation for the difference as:
L - W = 9
So, the linear system to model this situation is:
2L + 2W = 54
L - W = 9
To solve the system, we can use the method of substitution:
From the second equation, we can express L in terms of W:
L = W + 9
Substitute this expression for L in the first equation:
2(W + 9) + 2W = 54
2W + 18 + 2W = 54
4W + 18 = 54
4W = 54 - 18
4W = 36
W = 36/4
W = 9
Substitute this value of W in the second equation to find L:
L - 9 = 9
L = 9 + 9
L = 18
Therefore, the dimensions of the beach volleyball court are length (L) = 18 m and width (W) = 9 m.