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

1 answer

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.