Brenda is building a rectangular pen for her dog. She has enough fencing to build the pen so that it has a perimeter of 36 feet. She wants the pen to have an area of 65 ft2. What are the dimensions of the dog pen?
A. 5 feet by 13 feet
B. 10 feet by 8 feet
C. 9 feet by 9 feet
D. 65 feet by 1 foot
Since 65 = 5x13, try that to see whether it fits the required perimeter.
Only A and D could even possibly be a choice.
To find the dimensions of the dog pen, we can set up a system of equations using the given information.
Let's assume the length of the pen is L feet and the width is W feet.
The perimeter of a rectangular pen is given by the formula: P = 2L + 2W, where P is the perimeter.
Given that the perimeter is 36 feet, we can write the equation:
2L + 2W = 36
The area of a rectangular pen is given by the formula: A = L * W, where A is the area.
Given that the area is 65 ft^2, we can write the equation:
L * W = 65
Now, we have a system of equations:
2L + 2W = 36
L * W = 65
To solve this system of equations, we can use substitution or elimination. Let's use substitution.
From the first equation, we can solve for L in terms of W:
2L = 36 - 2W
L = 18 - W
Now, substitute L = 18 - W into the second equation:
(18 - W) * W = 65
Expand and rearrange the equation:
18W - W^2 = 65
Rearrange the terms:
W^2 - 18W + 65 = 0
Now, we can factor or use the quadratic formula to solve for W. Factoring the equation gives:
(W - 5)(W - 13) = 0
So, W = 5 or W = 13.
If W = 5, then L = 18 - W = 18 - 5 = 13.
If W = 13, then L = 18 - W = 18 - 13 = 5.
Therefore, the dimensions of the dog pen can be either 5 feet by 13 feet or 13 feet by 5 feet.
Looking at the answer choices, the correct answer is:
A. 5 feet by 13 feet.