Proving Similar Triangles Quick Check 2 of 52 of 5 Items Question Use the image to answer the question. 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 15 yards 15 yards 12 yards 12 yards 10 yards 10 yards Skip to navigation page 23 of 23 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

Answer 1

To find the length of \( YB \) using the properties of similar triangles, we can use the information given:

Given that \( \triangle XYZ \sim \triangle AYB \), the ratio of corresponding sides of similar triangles is equal.

The lengths we know are:

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

Let \( YB = x \). The ratio of the sides can be set up as:

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

Substituting the known values into the ratio:

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

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

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

Next, we can cross-multiply to find \( x \):

\[ 3x = 30 \]

Now divide both sides by 3:

\[ x = 10 \]

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

So the answer is:

10 yards