Question

The two triangles below are similar (but not drawn to scale). Find the value of
x . Round answer to the nearest tenth. triangle one is 30.6in and 25.8in. triangle two is 13.7 in and x.

Answer 1

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

Given:
- Triangle One has sides of \( 30.6 \) in and \( 25.8 \) in.
- Triangle Two has one side of \( 13.7 \) in and the other side is \( x \).

Since the two triangles are similar, the ratios of the lengths of the corresponding sides are equal. So we can write:

\[
\frac{30.6}{13.7} = \frac{25.8}{x}
\]

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

\[
30.6 \cdot x = 25.8 \cdot 13.7
\]

Calculating \( 25.8 \cdot 13.7 \):

\[
25.8 \cdot 13.7 = 352.26
\]

Now substitute back into the equation:

\[
30.6 \cdot x = 352.26
\]

To solve for \( x \), divide both sides by \( 30.6 \):

\[
x = \frac{352.26}{30.6}
\]

Calculating \( \frac{352.26}{30.6} \):

\[
x \approx 11.5
\]

So, the value of \( x \), rounded to the nearest tenth, is \( \boxed{11.5} \).