The ratio of the areas of two similar polygons is 64:36. If the perimeter of the first polygon is 35 cm, what is the perimeter of the second polygon?

Question

directrix · Answer

Theorem: If two polygons are similar, then the square of the scale factor of the two polygons is equal to the ratio of areas of the polygons.

So, 64/36 = (35/p)² where 35 is the perimeter of the first polygon and p is the perimeter of the second.

64/36 simplifies to 16/9.

16/9 = (35/p)²
You can take square roots of both sides and solve for p.

@Tiaraashley