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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

1 answer

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.