Big Ideas Math: Modeling Real Life, Grade 8
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Big Ideas Math: Modeling Real Life, Grade 8 View details
2. Solving Systems of Linear Equations by Substitution
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Exercise 15 Page 208

Recall the formulas for the perimeter and area of a rectangle.

1800 square feet, see solution.

Practice makes perfect
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!
180=2l+2w
180=2( 2w)+2w
Solve for w
180=4w+2w
180=6w
30=w
w=30
Now that we have a value for w, we can substitute it into either equation and solve for l. Let's substitute 30 for w in Equation (II) for simplicity.
l=2w
l=2( 30)
l=60
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.
A=l w
A= 60( 30)
1800
The volleyball court has an area of 1800 square feet.