lgebraic Expressions: Apply Try This You have 20 feet of fencing material to make a pen for your dog. The design of the pen is given as follows. Find the perimeter of the dog pen in terms of m and n . Will you be able to create a dog pen with the following dimensions? Explain your answers. m=3 feet by n=2 feet m=5.5 feet by n=3 feet m=7.5 feet by n=5.5 feet List the possible dimensions of the dog pen that you can make out of the available fencing material. Among the dimensions you listed, which should you use to make the dog pen? Explain your reasoning.
To find the perimeter of the dog pen, we need to add up the lengths of all the sides.
For the given design, we have two sides of length m and two sides of length n. Therefore, the perimeter P in terms of m and n is:
P = 2m + 2n
Now let's calculate the perimeters for the different dimensions:
For m = 3 feet and n = 2 feet:
P = 2(3) + 2(2) = 6 + 4 = 10 feet
For m = 5.5 feet and n = 3 feet:
P = 2(5.5) + 2(3) = 11 + 6 = 17 feet
For m = 7.5 feet and n = 5.5 feet:
P = 2(7.5) + 2(5.5) = 15 + 11 = 26 feet
Since we have 20 feet of fencing material, we can see that only the dimensions m = 3 feet and n = 2 feet satisfy the condition, with a perimeter of 10 feet. The other dimensions exceed the available material.
Therefore, the only possible dimensions for the dog pen are m = 3 feet and n = 2 feet, and this is the size we should use to make the dog pen.