Question

Polygon A is similar to polygon B. the sides of a polygon A are three times larger than the corresponding sides of polygon B. the perimeter od polygon A is 144. What is the perimeter of polygon B ?

A. 432
B. 12
C. 144
D. 48

Answer 1

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 =)