Question

The area of ΔABC is 9 cm², and the area of ΔDEF = 16 cm². If ΔABC ~ ΔDEF, find: perimeter (ΔABC) : perimeter (ΔABC).

Answer 1

Since △ABC ∼ △DEF,

`"Area of ΔABC"/"Area of ΔDEF" = ("side"_1/"side"_2)^2`

`9/16 = ("side"_1/"side"_2)^2`

`"side"_1/"side"_2 = sqrt(9/16)`

`"side"_1/"side"_2 = 3/4`

For similar triangles, the ratio of perimeters equals the ratio of corresponding side lengths.

∴ Perimeter of △ABC : Perimeter of △DEF = 3 : 4