Hi.
Let's start by recalling that the perimeter of a rectangle is calculated by adding the lengths of each long side (length) to the lengths of each short side (width). Since there are two long sides and two short sides in the rectangle:
P = 2L + 2W
We know from the problem that the long side is 7 units more than the short side. So L = W + 7.
Therefore, P for this rectangle (before we made it bigger) is:
P = 2(W+7) + 2W
P = 4W + 7
The problem does not tell us what the width is, so we are going to assume it is 1 unit. Therefore, P = 11. But this is not the final answer because we have to actually figure out the perimeter after we increase the size of the rectangle. So we are going to increase the smaller side (width) by 8 units and triple the length and then calculate the perimeter.
So:
P = 2W + 14 + 8 + 3(2W)
P = 2W + 22 + 6W
P = 8W + 22
Remember that we are assuming that width is 1 unit. So:
P = 8 + 22 = 30.
That is our final answer.
