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 39.5 inc and 14.3 inc. triangle two is x and 22.6 inc

Answer 1

Since the two triangles are similar, the ratios of the corresponding sides are equal.

Let's denote the sides of triangle one as follows:
- Side 1 = 39.5 inches
- Side 2 = 14.3 inches

And for triangle two:
- Side 1 = x inches
- Side 2 = 22.6 inches

We can set up the ratio:

\[
\frac{39.5}{x} = \frac{14.3}{22.6}
\]

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

\[
39.5 \times 22.6 = 14.3 \times x
\]

Calculating \(39.5 \times 22.6\):

\[
39.5 \times 22.6 = 893.7
\]

So, we have:

\[
893.7 = 14.3 \times x
\]

Now, we can solve for \(x\):

\[
x = \frac{893.7}{14.3}
\]

Calculating \( \frac{893.7}{14.3} \):

\[
x \approx 62.4
\]

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

\[
\boxed{62.4}
\]