Question

Triangle ABC is similar to triangle EFD. Whatscale factor is required to dllate triangle ABCso that its image, A' B'C', is congruent totriangle EFD?

Answer 1

Since triangles ABC and EFD are similar, their correponding sides are proportional.

We can see from the picture that side AB is equivalent to side EF. We can also see that side AC is equivalent to unknown side ED.

Since the triangles are similiar we can set the following ratio:

AB / EF = AC / ED

12 / 5 = 15 / ED

12 . ED = 5 . 15

12 . ED = 75

ED = 75 / 12

ED = 25 / 4

Let's check the scaling factor k must be:

AB / EF = 12 / 5

AC / ED = 15 / 25/4

AC / ED = 15 . 4 / 25

AC / ED = 60 / 25

AC / ED = 12 / 5

Since A'B'C' is congruent to EFD, then ABC must have the same scaling factor as above which is 12 / 5.

Answer: scaling factor = 12 / 5