Question

3. Brenda is building a rectangular pen for her dog. She

has enough fencing to build the pen so that its perimeter is
34 feet and its area is 60 feet. What are the dimensions of the
dog pen?

Answer 1

To find the dimensions of the rectangular pen, we can set up a system of equations using the perimeter and area formulas for a rectangle. Solving this system will give us the values of the length and width. The dimensions of the dog pen are approximately 4.5 feet by 9.5 feet.

Step-by-step explanation:

To find the dimensions of the rectangular pen, let's assume that the length is 'l' and the width is 'w'. We know that the perimeter of a rectangle is given by the formula: P = 2(l + w). Since the perimeter is given as 34 feet, we can set up the equation: 34 = 2(l + w).

The area of a rectangle is given by the formula: A = l * w. Since the area is given as 60 feet, we can set up the equation: 60 = l * w.

We now have a system of two equations with two variables. We can solve this system by substitution or elimination to find the values of 'l' and 'w'.

Substituting the value of w from the first equation into the second equation, we get: 60 = l * (34 - l).

Expanding and rearranging the equation, we get: l^2 - 34l + 60 = 0.

Solving this equation, we find that the dimensions of the dog pen are approximately 4.5 feet by 9.5 feet.