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 is 30.6in and 25.8in. triangle two is 13.7 in and x.
x=____in
x . Round answer to the nearest tenth. triangle one is 30.6in and 25.8in. triangle two is 13.7 in and x.
x=____in
Answers
GPT-4o mini
Since the triangles are similar, the ratios of their corresponding sides are equal. Let's denote the sides of triangle one as \( a = 30.6 \) in and \( b = 25.8 \) in, and the corresponding sides of triangle two as \( c = 13.7 \) in and \( d = x \).
The ratio of the sides can be established as follows:
\[
\frac{a}{c} = \frac{b}{d}
\]
Substituting in the known values:
\[
\frac{30.6}{13.7} = \frac{25.8}{x}
\]
To find \( x \), we can cross-multiply:
\[
30.6 \cdot x = 25.8 \cdot 13.7
\]
Calculating the right side:
\[
25.8 \cdot 13.7 = 352.26
\]
Now we have:
\[
30.6x = 352.26
\]
Next, divide both sides by \( 30.6 \):
\[
x = \frac{352.26}{30.6} \approx 11.5
\]
Thus, rounded to the nearest tenth:
\[
x \approx 11.5 \, \text{in}
\]
Therefore, the value of \( x \) is \( \boxed{11.5} \) inches.
The ratio of the sides can be established as follows:
\[
\frac{a}{c} = \frac{b}{d}
\]
Substituting in the known values:
\[
\frac{30.6}{13.7} = \frac{25.8}{x}
\]
To find \( x \), we can cross-multiply:
\[
30.6 \cdot x = 25.8 \cdot 13.7
\]
Calculating the right side:
\[
25.8 \cdot 13.7 = 352.26
\]
Now we have:
\[
30.6x = 352.26
\]
Next, divide both sides by \( 30.6 \):
\[
x = \frac{352.26}{30.6} \approx 11.5
\]
Thus, rounded to the nearest tenth:
\[
x \approx 11.5 \, \text{in}
\]
Therefore, the value of \( x \) is \( \boxed{11.5} \) inches.