Question

If XYZ ~ AYB, AND XY= 24 YARDS, YZ= 30 YARS, AND YA= 8 YARS, THEN WHAT IS THE LENGTH OF YB?

Answer 1

Given that triangles \( XYZ \) and \( AYB \) are similar (denoted as \( XYZ \sim AYB \)), we can use the properties of similar triangles. The lengths of corresponding sides are in proportion.

From the problem, we have the following lengths:

- \( XY = 24 \) yards
- \( YZ = 30 \) yards
- \( YA = 8 \) yards

Since triangles \( XYZ \) and \( AYB \) are similar, we can set up a proportion between the corresponding sides:

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

Substituting the known values into the proportion:

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

Now simplify the left side:

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

Next, we can solve for \( YB \) by cross-multiplying:

\[
3 \cdot YB = 30
\]

Then, divide both sides by 3:

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

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