Since the field is in rectangular shape, its area can be found by multiplying the length by the width.
B
b
Begin by substituting the given value into the equation that you wrote Part A. Then solve the equation by factoring.
A
a
Variable: l is the length of the soccer field.
Equation: A=l^2-45l
B
b
Lenght: 120 yd
Width: 75 yd
Practice makes perfect
a
The width of a high school soccer field is 45 yards shorter than its length as shown below.
We see above that the variable l represents the length of the field. Since the field has the shape of a rectangle, its area A can be calculated by multiplying the length by the width.
A=l(l-45) ⇔ A=l^2-45l
b
Given that the area of the field is 9000 square yards, let's first substitute 9000 for A into the equation we wrote in Part A. Then, we will solve the equation by factoring and using the Zero Product Property.
Since the length cannot be negative, we will ignore the negative value of l. Therefore, we can determine the dimensions of the field as shown below.
Length:& 120 yd
Width:& 120-45=75 yd
