Triangle ABC has the following side lengths:

AB = 5 ft, BC = 10 ft, CA = 12 ft

Triangle DEF is similar to triangle ABC.
The shortest side of triangle DEF, DE = 8.5 ft.

What are the lengths for the other two sides of triangle DEF?

A. EF 17 ft; FD = 20.4 ft
B. EF = 6 ft; FD = 7.2 ft
C. EF = 10 ft; FD = 12 ft
D. EF = 20 ft; FD = 24 ft

Question

Triangle ABC has the following side lengths: 

AB = 5 ft, BC = 10 ft, CA = 12 ft

Triangle DEF is similar to triangle ABC. 
The shortest side of triangle DEF, DE = 8.5 ft.

What are the lengths for the other two sides of triangle DEF?

	A.	EF 17 ft; FD = 20.4 ft
	B.	EF = 6 ft; FD = 7.2 ft
	C.	EF = 10 ft; FD = 12 ft
	D.	EF = 20 ft; FD = 24 ft

anonymous · Answer

Set up a proportion.
Find the corresponding sides.

directrix · Answer

Triangle DEF is similar to triangle ABC. 

Lengths of corresponding sides of similar triangles are in proportion.

Given the triangle similarity statement,

AB/DE = AC/DF = BC/EF

Using the given values,

5/8.5 = 12/DF = 10/EF

Take the first two equal ratios,

5/8.5 = 12/DF

Cross multiply and solve for DF

DF = 20.4

Then, do the same for the equal ratios to solve for EF.

5/8.5 =10/EF

@arlira