Question

If XYZ~AYB, and XY=24 yard, YZ=30 yards, and YA=8 yards, then what is the length of YB?

25 yards
15 yards
10 yards
12 yards

Answer 1

To find the length of \( YB \), we can use the similarity of triangles, given that \( XYZ \sim AYB \).

The sides of the triangles are proportional, which gives us the following relationship:

\[
\frac{XY}{YA} = \frac{YZ}{YB}
\]

We know:
- \( XY = 24 \) yards
- \( YZ = 30 \) yards
- \( YA = 8 \) yards
- \( YB = ? \)

Now, substituting the known values into the proportion:

\[
\frac{24}{8} = \frac{30}{YB}
\]

Now simplify \( \frac{24}{8} \):

\[
\frac{24}{8} = 3
\]

So, we have:

\[
3 = \frac{30}{YB}
\]

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

\[
3 \cdot YB = 30
\]

Now divide both sides by 3:

\[
YB = \frac{30}{3} = 10 \text{ yards}
\]

Thus, the length of \( YB \) is \( \boxed{10} \) yards.