Question

The two triangles below are similar (but not drawn to scale). Find the value of x . Round answer to the nearest tenth.
one is 38.1 in and 17 in. two is x and 23in.
x=-----in

Answer 1

To solve for \( x \) in the two similar triangles, we can set up a proportion using the corresponding side lengths of the triangles.

Let's denote the two triangles as Triangle 1 and Triangle 2.

The sides are given as follows:
- For Triangle 1: 38.1 inches (corresponding side) and 17 inches (corresponding side).
- For Triangle 2: \( x \) inches (unknown side) and 23 inches (corresponding side).

Since the triangles are similar, we can set up the proportion:

\[
\frac{38.1}{17} = \frac{x}{23}
\]

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

\[
38.1 \cdot 23 = 17 \cdot x
\]

Calculating \( 38.1 \cdot 23 \):

\[
38.1 \cdot 23 = 876.3
\]

Now we can plug that back into the equation:

\[
876.3 = 17x
\]

Next, we solve for \( x \) by dividing both sides by 17:

\[
x = \frac{876.3}{17}
\]

Calculating \( \frac{876.3}{17} \):

\[
x \approx 51.0 \text{ inches}
\]

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

\[
\boxed{51.0 \text{ in}}
\]