Similar Triangles: Finding Perimeter of ΔDEF When ΔABC Perimeter is 64

Question

$ΔDEF∼Δ\text{ABC}$

If the perimeter of $ΔABC$ is 64, then what is the perimeter of $ΔDEF$ ?

00:00 Find the perimeter of the triangle according to the similarity ratio

00:03 The triangles are similar according to the given data

00:07 We want to find the similarity ratio

00:11 Let's substitute the side values according to the given data and solve

00:15 We'll factor each number with factor (6) and reduce

00:19 This is the similarity ratio between the triangles

00:23 The perimeter ratio equals the similarity ratio

00:29 Let's substitute appropriate values and solve to find the triangle's perimeter

00:37 We'll multiply by the reciprocal to isolate P

00:48 And this is the solution to the question