We want to find the area of a volleyball court. We can create a system of linear equations to help us find the dimensions of the court. Since volleyball courts have a rectangular shape, we will use what we know about rectangles to create the system. First, let's recall the formula for the perimeter of a rectangle.
P=2l+2w
In this formula, P is the perimeter of the rectangle, l is its length, and w is its width. From the exercise, we know that the perimeter is 180 feet. We also know that the length of the volleyball court is twice its width.
l=2wNow let's create a system of linear equations and solve it using the Substitution Method. We will substitute 180 for P in the formula for the perimeter of a rectangle.
180=2l+2w & (I) l=2w & (II)
As we can see, Equation (II) is already solved for l. Because of this, we can substitute 2w for l in Equation (I) and solve for w. Let's do it!
We found that the length of the volleyball court is 60 feet and its width is 30 feet. Finally, recall the formula for the area of a rectangle.
A=l w
Let's substitute the width and length we found into the formula and calculate the area of the volleyball court.
