Question
The two triangles below are similar (but not drawn to scale). Find the value of
x
x . Round answer to the nearest tenth.
30.6 inches
20.6 inches
x
x 16.9 inches
x
=
x =
inches
Answers
GPT-4o mini
Since the triangles are similar, we can use the property of similar triangles, which states that the ratios of corresponding sides are equal.
Given the triangles, we can set up a proportion using the lengths of the corresponding sides:
\[
\frac{x}{20.6} = \frac{16.9}{30.6}
\]
Now, we can multiply both sides by \(20.6\) to solve for \(x\):
\[
x = 20.6 \cdot \frac{16.9}{30.6}
\]
Calculating the right side, we first find \(\frac{16.9}{30.6}\):
\[
\frac{16.9}{30.6} \approx 0.5513
\]
Now, we multiply by \(20.6\):
\[
x \approx 20.6 \cdot 0.5513 \approx 11.35
\]
Rounding to the nearest tenth:
\[
x \approx 11.4 \text{ inches}
\]
So, the value of \(x\) is approximately \(11.4\) inches.
Given the triangles, we can set up a proportion using the lengths of the corresponding sides:
\[
\frac{x}{20.6} = \frac{16.9}{30.6}
\]
Now, we can multiply both sides by \(20.6\) to solve for \(x\):
\[
x = 20.6 \cdot \frac{16.9}{30.6}
\]
Calculating the right side, we first find \(\frac{16.9}{30.6}\):
\[
\frac{16.9}{30.6} \approx 0.5513
\]
Now, we multiply by \(20.6\):
\[
x \approx 20.6 \cdot 0.5513 \approx 11.35
\]
Rounding to the nearest tenth:
\[
x \approx 11.4 \text{ inches}
\]
So, the value of \(x\) is approximately \(11.4\) inches.