Question

If triangle ABC is similar to triangle XBY, and line AB =16 cm, line AC= 8 cm, and line XY =6 cm, then what is the length of line BX?

Answer 1

Given that triangle ABC is similar to triangle XBY, we can use the properties of similar triangles to set up a proportion based on corresponding sides.

Let's denote the sides of triangle ABC:
- \( AB = 16 \) cm
- \( AC = 8 \) cm

Correspondingly, we have the side of triangle XBY:
- \( XY = 6 \) cm

Since the triangles are similar, the ratios of their corresponding sides are equal. We can write the following proportion using the sides \( AB \) and \( XY \):

\[
\frac{AB}{XY} = \frac{AC}{BX}
\]

Plugging in the known values:

\[
\frac{16}{6} = \frac{8}{BX}
\]

Now we simplify the left side:

\[
\frac{16}{6} = \frac{8}{3}
\]

Thus, our proportion now looks like:

\[
\frac{8}{3} = \frac{8}{BX}
\]

Next, we cross-multiply to solve for \( BX \):

\[
8 \cdot BX = 8 \cdot 3
\]
\[
8BX = 24
\]
\[
BX = \frac{24}{8} = 3 \, \text{cm}
\]

Therefore, the length of line \( BX \) is \( \boxed{3} \) cm.