Since similar polygons have proportional sides, their perimeters are proportional as well. Set up a ratio to find the answer:
Side x of polygon A is to side y of polygon B as the perimeter of A is to the perimeter of B.
In mathematical terms:
x:y = A:B
We know that one side of A is 3 times as large as one side of B, so we can substitute x and y for those values:
3:1 = A:B
We also know that the perimeter of A is 144, so we can substitute that value as well.
3:1 = 144:B
Now we can use this proportion to find the perimeter of B. Multiply the means and extremes and solve:
3B = 144
B = 48
The perimeter of polygon B is 48.
I hope this helps =)
