Question

Patricia is making a dog pen in her back yard. The pen will be rectangular and have an area of 24 square feet. Draw and label a diagram that shows all possible whole-number dimensions for the pen. Find the perimeter of each rectangle you drew. Which dimensions should Patricia use in order to spend the least amount of money on fencing material? Explain your reasoning.

Answer 1

I understand how to solve polynomials, but I don't even know how to approach this

Answer 2

Since the pen is rectangular, its area is the length times the width.
There are many possible lengths and widths that will give an area of 24 sq ft. Any two numbers whose product is 24 will work.
For example, 24 ft by 1 ft, 48 ft by 0.5 ft, etc.
The problem is only interested in lengths and widths that are whole numbers, so from my examples above, 24 ft by 1 ft is acceptable, but 48 ft by 0.5 ft is not.
What are the other whole-number lengths and widths that will give an area of 24?
Come up with all the different length and width possibilities.
Then find the perimeter of each of those choices.
Then since she wants to spend the least amount on fencing the pen, choose the one with the smallest perimeter.

Answer 3

Oh my goodness thank you sooooo much! I understand this now!!!! How should I draw a diagram expressing this?

Answer 4

Draw the rectangles that have whole-number length and width, and label the length and width in each rectangle.
In addition to the 24 ft by 1 ft rectangle, which others did you come up with?

Answer 5

I got the answer. The dimensions are 6x4. Perimeter is 20. Thanks so much for your help!

Answer 6

You're welcome