Question

The two triangles below are similar (but not drawn to scale). Find the value of x . Round answer to the nearest tenth.

33.1 inches
20.9 inches

right shape is 17 inchers and x

Answer 1

To determine the value of \( x \) in the similar triangles, we'll use the property of similar triangles that states the ratios of corresponding sides are equal.

Let's denote the sides of the triangles:

1. For the larger triangle, the sides are 33.1 inches and 20.9 inches.
2. For the smaller triangle, the sides are 17 inches and \( x \).

Setting up the proportion using the corresponding sides, we have:

\[
\frac{33.1}{17} = \frac{20.9}{x}
\]

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

\[
33.1 \cdot x = 20.9 \cdot 17
\]

Calculating \( 20.9 \cdot 17 \):

\[
20.9 \cdot 17 = 355.3
\]

Now we have:

\[
33.1x = 355.3
\]

Next, we solve for \( x \) by dividing both sides by 33.1:

\[
x = \frac{355.3}{33.1} \approx 10.7
\]

Rounding to the nearest tenth, we find:

\[
x \approx 10.7 \text{ inches}
\]

Thus, the value of \( x \) is approximately **10.7 inches**.