△ABC ∼ △DEF. Their scale factor of △ABC to △DEF is 7:9. If the perimeter of △ABC is 42 cm, then find the perimeter of △DEF.

Answer 1

If the 2 triangles are similar and ABC:DEF = 7:9, then perimeter of ABC:perimeter of DEF = 7:9

We know the perimeter of ABC = 42, plug that into the ratios in the previous sentence.

42/perimDEF = 7/9

Cross multiply

42 × 9 = 7 × perimeter DEF

378 = 7 × perimeter DEF

÷7. ÷7

perimeter DEF = 54

Answer 2

The ratio of the scale factor will equal the ratio of their perimeters so

7 = 42

--- ----

9 x

where x is the perimeter of DEF

cross-multiply

7x = 9*42

x = 9*6

x = 54