The two triangles below are similar (but not drawn to scale). Find the value of

Question

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:

\[ \boxed{12.6} \]