Question

How do i do this? Picture below...

Answer 1

The answers are... 12, 9 7.2 or 20

Answer 2

similar triangles have corresponding sides in the same ratio

Answer 3

"corresponding sides" are those that are opposite the same angle

Answer 4

Ok, but I don't know what to do next?

Answer 5

well - first identify the corresponding sides between the two similar triangles.

Answer 6

e.g. which side corresponds to DE?

Answer 7

c?

Answer 8

C is not a side

Answer 9

d and c?

Answer 10

side DE of triangle CDE corresponds to side ?? of triangle ABC

Answer 11

a and b

Answer 12

we usually say AB rather than a and b

Answer 13

ok, now we know DE and AB are corresponding sides.

can you find two other corresponding sides?

Answer 14

AC and EC?

Answer 15

perfect!

Answer 16

now use the rule for similar triangles that states the ratio of corresponding sides is the same. this gives us:\[\frac{DE}{AB}=\frac{EC}{AC}\]fill-in all the known length and then solve to find DE

Answer 17

*known lengths

Answer 18

\[ \frac{ DE }{ 24 } = \frac{ 15 }{ 40 }\]

Answer 19

that is correct - now use that to solve for DE

Answer 20

9

Answer 21

perfect! well done! :)

Answer 22

Thank you so much! thank you you have been an amazing help!

Answer 23

yw - I'm glad I was able to help. :)