Triangle ABC ~ triangle DEF. Use the image to answer the question.

Question

a triangle ABC with side AB labeled 11, side CA labeled 7.6 and side BC labeled 7.9 and a second triangle DEF with side DE labeled 2.2

Determine the measurement of EF.
EF = 1.58
EF = 1.52
EF = 1.1
EF = 5.5

Answer 1

Since triangles ABC and DEF are similar (denoted as \( \triangle ABC \sim \triangle DEF \)), the corresponding sides of the triangles are in proportion.

The sides given for triangle ABC are:

• AB = 11
• CA = 7.6
• BC = 7.9

The side DE of triangle DEF is given as:

• DE = 2.2

We need to find the length of side EF in triangle DEF. Let's set up a proportion using the sides of the similar triangles.

Using the sides AB and DE, we can write the proportion:

\[ \frac{AB}{DE} = \frac{BC}{EF} \]

Substituting the known values into the proportion:

\[ \frac{11}{2.2} = \frac{7.9}{EF} \]

Now, calculate \( \frac{11}{2.2} \):

\[ \frac{11}{2.2} = 5 \]

Now we can rewrite the proportion:

\[ 5 = \frac{7.9}{EF} \]

To find EF, we cross-multiply:

\[ 5 \cdot EF = 7.9 \]

Now, solve for EF:

\[ EF = \frac{7.9}{5} = 1.58 \]

Thus, the measurement of EF is:

\[ \boxed{1.58} \]