If △XYZ∼△AYB , and XY¯¯¯¯¯¯¯¯=24 yards, YZ¯¯¯¯¯¯¯=30 yards, and YA¯¯¯¯¯¯¯¯=8 yards, then what is the length of YB¯¯¯¯¯¯¯¯ ? (1 point) Responses 25 yards 25 yards 10 yards 10 yards 12 yards 12 yards 15 yards 15 yards

Answer 1

Given that triangles \( \triangle XYZ \sim \triangle AYB \), we can use the property of similar triangles where corresponding sides are proportional.

From the information given:

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

We need to find \( YB \).

Since the triangles are similar, we can write the ratio of the sides as follows:

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

Now, we substitute the known lengths into the ratio:

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

Simplify the left side:

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

Now cross-multiply:

\[ 3 \cdot YB = 30 \]

Solving for \( YB \):

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

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