Question

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

33.1 inches
20.9 inches for smaller triangle

is 17 inchers and x for smaller triangle

Answer 1

To solve for \( x \) in the similar triangles, we can use the property that the ratios of corresponding sides of similar triangles are equal.

Given:
- Larger triangle sides: 33.1 inches and 17 inches
- Smaller triangle sides: 20.9 inches and \( x \)

We can set up a proportion based on the corresponding sides:

\[
\frac{33.1}{20.9} = \frac{17}{x}
\]

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

\[
33.1 \times x = 20.9 \times 17
\]

Calculating \( 20.9 \times 17 \):

\[
20.9 \times 17 = 355.3
\]

Now we can plug that back into our equation:

\[
33.1x = 355.3
\]

Now, divide both sides by 33.1 to isolate \( x \):

\[
x = \frac{355.3}{33.1}
\]

Calculating \( \frac{355.3}{33.1} \):

\[
x \approx 10.7
\]

So, the value of \( x \) rounded to the nearest tenth is:

\[
\boxed{10.7} \text{ inches}
\]