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

Question

𝑥
x . Round answer to the nearest tenth. Click Here for Help Video

35 inches


23.2 inches
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x 10.2 inches


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=
x =
inches

Answer 1

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

Let’s use the lengths of the sides provided:

1. For the triangles, we have:
   • One side from the first triangle: 35 inches
   • Corresponding side from the second triangle: 23.2 inches
   • The unknown side in the second triangle: \( x \)
   • Corresponding side in the first triangle: 10.2 inches

According to the property of similar triangles, the ratios of the corresponding sides are equal:

\[ \frac{35}{23.2} = \frac{x}{10.2} \]

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

\[ 35 \cdot 10.2 = 23.2 \cdot x \]

Calculating \( 35 \cdot 10.2 \):

\[ 35 \cdot 10.2 = 357 \]

So our equation now looks like:

\[ 357 = 23.2 \cdot x \]

To isolate \( x \), divide both sides by 23.2:

\[ x = \frac{357}{23.2} \]

Calculating \( \frac{357}{23.2} \):

\[ x \approx 15.4 \]

Thus, rounding to the nearest tenth:

\[ \boxed{15.4} \] inches.