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



35 inches


23.2 inches
𝑥
x 10.2 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.

Let’s use the lengths of the sides provided:

1. For the triangles, we have:
- One side from the first triangle: 35 inches
- Corresponding side from the second triangle: 23.2 inches
- The unknown side in the second triangle: \( x \)
- Corresponding side in the first triangle: 10.2 inches

According to the property of similar triangles, the ratios of the corresponding sides are equal:

\[
\frac{35}{23.2} = \frac{x}{10.2}
\]

Now, we can cross-multiply to solve for \( x \):

\[
35 \cdot 10.2 = 23.2 \cdot x
\]

Calculating \( 35 \cdot 10.2 \):

\[
35 \cdot 10.2 = 357
\]

So our equation now looks like:

\[
357 = 23.2 \cdot x
\]

To isolate \( x \), divide both sides by 23.2:

\[
x = \frac{357}{23.2}
\]

Calculating \( \frac{357}{23.2} \):

\[
x \approx 15.4
\]

Thus, rounding to the nearest tenth:

\[
\boxed{15.4}
\] inches.