Question

Dora says that of all the possible rectangles with the same area, the rectangle with the largest perimeter will have two side lengths that are 1 unit does her sentment make sense?

Answer 1

Answer:

  maybe

Step-by-step explanation:

Dora is apparently assuming the dimensions are integers. In that case she is correct.

If the dimensions are unconstrained, the perimeter will be largest when a pair of opposite sides will be the smallest measure allowed.

For some perimeter P and side length x, the area is ...

  A = x(P/2 -x)

Conversely, the perimeter for a given area is ...

  P = 2(A/x +x)

This gets very large when x gets very small, so Dora is correct in saying that the side lengths that are as small as they can be will result in the largest perimeter. We have no way of telling if her assumption of integer side lengths is appropriate. If it is not, her statement makes no sense.