Question

Use the image to answer the question. What is the length of x in decimal form to the nearest hundredth? (1 point)

first triangle side a- 11.4 side b- 18
second triangle side a- __ side b - 23.4

Answer 1

To find the length of \( x \) in the second triangle, it appears we're trying to find a relationship between the two triangles involving their sides. It seems you might be using the concept of proportion based on similar triangles.

According to the dimensions given:

1. First triangle: Side \( a = 11.4 \), Side \( b = 18 \)
2. Second triangle: Side \( a = x \), Side \( b = 23.4 \)

We can set up a proportion based on the similarity of the triangles:

\[
\frac{a_1}{b_1} = \frac{a_2}{b_2}
\]

Substituting the known values:

\[
\frac{11.4}{18} = \frac{x}{23.4}
\]

To find \( x \), cross-multiply:

\[
11.4 \times 23.4 = 18 \times x
\]

Calculating the left side:

\[
11.4 \times 23.4 = 267.96
\]

Now we set up the equation:

\[
267.96 = 18x
\]

Now, solve for \( x \):

\[
x = \frac{267.96}{18} \approx 14.88
\]

Rounding to the nearest hundredth, the length of \( x \) is:

\[
\boxed{14.88}
\]