Question

The two triangles below are similar (but not drawn to scale). Find the value of
x . Round answer to the nearest tenth.
for the big triangle 32.6 inches side 26.7 inches bottom
for small triangle 15.4 side x bottom

Answer 1

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

Given the dimensions:

- Large triangle:
- Side = 32.6 inches
- Bottom = 26.7 inches
- Small triangle:
- Side = 15.4 inches
- Bottom = \( x \)

We establish the proportion:

\[
\frac{32.6}{15.4} = \frac{26.7}{x}
\]

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

\[
32.6x = 15.4 \cdot 26.7
\]

Calculating \( 15.4 \cdot 26.7 \):

\[
15.4 \cdot 26.7 = 411.18
\]

So the equation becomes:

\[
32.6x = 411.18
\]

Now, divide both sides by \( 32.6 \):

\[
x = \frac{411.18}{32.6}
\]

Calculating \( \frac{411.18}{32.6} \):

\[
x \approx 12.6
\]

Finally, rounding to the nearest tenth, we have:

\[
\boxed{12.6}
\]