Question Two polygons are similar. The perimeter of the larger polygon is 120 yards and the ratio of the corresponding side lengths is 1/6 . Find the perimeter of the other polygon.

Answer 1

Recall the rule of similarity: the angles are equal but the sides are not. BUT the sides will be proportional because the angles are equal.

so let’s say the polygon is a triangle:

triangle 1 has sides A, B, C

triangle 2 has sides X, Y, Z

because they are similar and we know the ratio is 1/6, we CS an say that

perimeter 1 = A + B + C = 120

we know each side is proportionate as well, so

X = A* 1/6, Y = B * 1/6, Z = C * 1/6

perimeter (2) = X + Y + Z

substituting, we get

perimeter (2)= A* 1/6 + B*1/6 + C*1/6

perimeter(2) = 1/6(A+B+C) = 1/6 * 120

perimeter (2) = 20 yards

i hope this helps your understanding better. Let me know if you would like to schedule a lesson l. I’d be happy to help!

Answer 2

120 x 1/6 = 20 yards