Question

The two triangles below are similar (but not drawn to scale). Find the value of
𝑥
x . Round answer to the nearest tenth. Click Here for Help Video












30.7 inches


12.2 inches
𝑥
x 22.1 inches





𝑥

=
x =
inches

Answer 1

To solve for \( x \) in the similar triangles, we can set up a proportion based on the corresponding sides of the triangles.

Given:

- Triangle 1: \( 30.7 \) inches (corresponds to \( 22.1 \) inches)
- Triangle 2: \( x \) inches (corresponds to \( 12.2 \) inches)

We can set up the following proportion:

\[
\frac{30.7}{22.1} = \frac{x}{12.2}
\]

Now we can cross-multiply:

\[
30.7 \times 12.2 = 22.1 \times x
\]

Calculating the left side:

\[
30.7 \times 12.2 = 374.54
\]

So now we have:

\[
374.54 = 22.1 \times x
\]

Next, we can solve for \( x \):

\[
x = \frac{374.54}{22.1}
\]

Calculating \( x \):

\[
x \approx 16.9
\]

Thus, the value of \( x \) is approximately:

\[
\boxed{16.9} \text{ inches}
\]

Make sure to round to the nearest tenth as asked, which we've done.