Question

The triangles shown are similar. Use the image to answer the question.

a triangle DEF with side DF labeled 10 and a second overlapping triangle GEH with side GH labeled 4 and EH labeled 8

Determine the length of side FE.
20
12
10
8

Answer 1

Since triangles DEF and GEH are similar, we can use the properties of similar triangles to find the length of side FE.

From the information given:
- Side DF in triangle DEF is 10.
- Side GH in triangle GEH is 4.
- Side EH in triangle GEH is 8.

The sides of similar triangles are proportional. Therefore, we can set up a proportion based on the corresponding sides:

\[
\frac{DF}{GH} = \frac{FE}{EH}
\]

Substituting the known values into the proportion gives us:

\[
\frac{10}{4} = \frac{FE}{8}
\]

Now, we can cross-multiply to solve for FE:

\[
10 \cdot 8 = 4 \cdot FE
\]

This simplifies to:

\[
80 = 4 \cdot FE
\]

Dividing both sides by 4 gives:

\[
FE = \frac{80}{4} = 20
\]

Thus, the length of side FE is **20**.