Question

1. diagram with a slanted line, vertical segments labeled 40, x, and horizontal segments labeled 32, 14 (axes with arrows).

Explanation:

Answer:

To solve for \( x \), we can use similar triangles. The ratios of corresponding sides should be equal. So we set up the proportion:

\[
\frac{40}{32} = \frac{x}{14}
\]

Cross - multiply to get:

\[
32x = 40\times14
\]

\[
32x = 560
\]

Divide both sides by 32:

\[
x=\frac{560}{32}=\frac{35}{2} = 17.5
\]

So the value of \( x \) is \( 17.5 \) (or \( \frac{35}{2} \)).