Question

5 of 225 of 22 Items








Question


If △XYZ∼△AYB
, and YB = 26 ft, YA = 14 ft and YZ = 92 ft, then what is they length of YX¯¯¯¯¯¯¯¯
?



(1 point)
Responses

39.56 ft
39.56 ft

56.32 ft
56.32 ft

170.86 ft
170.86 ft

49.53 ft
49.53 ft
Skip to navigation

Answer 1

To solve for the length of \( YX \) in the triangles \( △XYZ \sim △AYB \), we can use the property of similar triangles that states the ratios of corresponding sides are equal.

Given:
- \( YB = 26 \) ft
- \( YA = 14 \) ft
- \( YZ = 92 \) ft

Since the triangles are similar, we can set up the proportion based on the corresponding sides:

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

Substituting the known values into the equation:

\[
\frac{92}{14} = \frac{YX}{26}
\]

Now, we can cross-multiply to solve for \( YX \):

\[
92 \times 26 = 14 \times YX
\]

Calculating \( 92 \times 26 \):

\[
92 \times 26 = 2392
\]

So, we have:

\[
2392 = 14 \times YX
\]

Dividing both sides by 14:

\[
YX = \frac{2392}{14} = 170.86 \text{ ft}
\]

Thus, the length of \( YX \) is **170.86 ft**.

The correct response is **170.86 ft**.