Question
The two triangles below are similar (but not drawn to scale). Find the value of x . Round answer to the nearest tenth. triangle one lines are 31.7 inc and 21.8 inc. triangle two line are x and 13.2inc
Answers
GPT-4o mini
To find the value of \( x \) in the two similar triangles, we can use the property of similar triangles which states that the ratios of the corresponding sides are equal.
Given the sides of the triangles:
- Triangle 1: \( 31.7 \, \text{in} \) and \( 21.8 \, \text{in} \)
- Triangle 2: \( x \) and \( 13.2 \, \text{in} \)
The ratio of the sides can be set up as follows:
\[
\frac{31.7}{x} = \frac{21.8}{13.2}
\]
We can cross-multiply to solve for \( x \):
\[
31.7 \cdot 13.2 = 21.8 \cdot x
\]
Calculating the left-hand side:
\[
31.7 \cdot 13.2 = 418.44
\]
Now we can rewrite the equation:
\[
418.44 = 21.8 \cdot x
\]
To isolate \( x \), divide both sides by \( 21.8 \):
\[
x = \frac{418.44}{21.8}
\]
Calculating the right-hand side:
\[
x \approx 19.16
\]
Rounding to the nearest tenth, we find:
\[
x \approx 19.2
\]
Thus, the value of \( x \) is approximately **19.2 inches**.
Given the sides of the triangles:
- Triangle 1: \( 31.7 \, \text{in} \) and \( 21.8 \, \text{in} \)
- Triangle 2: \( x \) and \( 13.2 \, \text{in} \)
The ratio of the sides can be set up as follows:
\[
\frac{31.7}{x} = \frac{21.8}{13.2}
\]
We can cross-multiply to solve for \( x \):
\[
31.7 \cdot 13.2 = 21.8 \cdot x
\]
Calculating the left-hand side:
\[
31.7 \cdot 13.2 = 418.44
\]
Now we can rewrite the equation:
\[
418.44 = 21.8 \cdot x
\]
To isolate \( x \), divide both sides by \( 21.8 \):
\[
x = \frac{418.44}{21.8}
\]
Calculating the right-hand side:
\[
x \approx 19.16
\]
Rounding to the nearest tenth, we find:
\[
x \approx 19.2
\]
Thus, the value of \( x \) is approximately **19.2 inches**.