b The perimeter is the sum of its four sides. The area is the product of the pen's width and length.
C
c Solve either equation from Part B. Then use that information to find the length.
A
a See solution.
B
bPerimeter: 100=8w-4
Area: 481=3w^2-2w
C
cLength: 37 feet
Width: 13 feet
Practice makes perfect
a We are told that a farmer builds a rabbit pen from a length of wire. Let's label the length as l and the width as w. With this information, we can draw the following diagram representing the pen.
From the exercise we know that the length of the pen is two feet less than three times its width. With this information, we can write the following function for describing the length.
l=3w-2
Let's replace l with this expression.
b In Part A we defined the dimensions of the pen. We have also been given the perimeter and the area of the pen as P= 100 and A= 481, respectively. Let's write one equation describing the pen's perimeter. This is the sum of its four sides.
Perimeter
100=2(3w-2)+2w
⇓
100=8w-4
We can also write an expression for its area, which is the product of its two sides.
Area
481=w(3w-2)
⇓
481=3w^2-2w
c To determine the dimensions of the pen, we must solve one of the equations we wrote in Part A. Let's use the expression for the perimeter, as this does not involve a squared variable.
