f △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

1 answer

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

The ratios of the sides can be set up as follows:

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

Now, we know the lengths:

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

Let \( YB \) be \( x \). Therefore, we can set up the proportions:

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

Now, simplifying the left side:

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

So, we have:

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

Cross-multiplying gives us:

\[ 3x = 30 \]

Now dividing both sides by 3:

\[ x = 10 \]

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

The correct answer is:

10 yards.