Question

Polygon ABCDEF is similar to polygon GHIJKL. If side AB is 12, x, plus, 6, x12x+6x and side GH is 8, x, plus, 4, x8x+4x, and these sides are corresponding sides, what is the ratio of the perimeter of polygon GHIJKL to the perimeter of polygon ABCDEF?

Answer 1

Similarity means the perimeters scale like any pair of corresponding sides. So the ratio = GH/AB = (8x+4)/(12x+6).

Factor: (8x+4)=4(2x+1), (12x+6)=6(2x+1), so the ratio = 4/6 = 2/3 (provided 2x+1 ≠ 0, i.e. x ≠ −1/2).