Question

Logan has 64 inches of trim to make a picture frame. Since he wants to use all of the trim, he decides to make a square frame measuring 8 inches on each side. Did Logan correctly determine the correct frame size? Explain.

Answer 1

For this problem, we need to identify whether Logan successfully created a frame that could use 64 inches of trim, if the frame has 8 inches on each side.

In order to determine the total amount of trim used, we need to calculate the perimeter of the frame, which is the sum of all the sides. We have:

`P=8+8+8+8=32\text{ inches}`

Therefore logan did not use all the trim, because he had 64 inches to use. To correctly use all the trim, he'd need to have a frame with dimensions:

`d=(64)/(4)=16\text{ inches}`

He'd need to have a square frame measuring 16 inches on each side, because a frame like that would have a perimeter of 64 inches.