Question

Triangles ABC and DEF are similar triangles. What are the lengths of the unknown sides?

Answer 1

Answer:

D

Step-by-step explanation:

Similar triangles have corresponding sides that are proportional.

• AC is corresponding side to DF
• AB is corresponding side to DE
• BC is corresponding side to EF

From the 2 given corresponding sides, AB = 8 and DE = 12, we can figure out their proportionality.

$\frac{AB}{DE}=\frac{8}{12}=\frac{2}{3}$

So all corresponding sides of the first triangle to the second triangle will have a ratio of 2:3.

So,

$\frac{AC}{DF}=\frac{10}{DF}=\frac{2}{3}\\10*3=2DF\\DF=\frac{30}{2}=15$

DF = 15

And,

$\frac{BC}{EF}=\frac{6}{EF}=\frac{2}{3}\\6*3=2EF\\EF=\frac{18}{2}=9$

EF = 9

Answer choice D is right.