Question

If ^XYZ ~^AY B, and YB= 25ft, YA= 16ft, and YZ = 88ft, then what is the length of YX?

Answer 1

Since triangles \(^XYZ\) and \(^AYB\) are similar (denoted as \(^XYZ \sim ^AYB\)), we can use the properties of similar triangles to establish a relationship between their corresponding sides.

Let’s assign the corresponding sides:

- \(YZ\) corresponds to \(AB\)
- \(YX\) corresponds to \(AY\)
- \(XY\) corresponds to \(YB\)

From the problem, we know:

- \(YB = 25 \text{ ft}\)
- \(YA = 16 \text{ ft}\)
- \(YZ = 88 \text{ ft}\)

Using the properties of similar triangles, we can set up the following proportion based on the corresponding sides:

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

Substituting the given values into the proportion:

\[
\frac{YX}{16} = \frac{88}{25}
\]

Now, we can solve for \(YX\):

\[
YX = 16 \times \frac{88}{25}
\]

Calculating that:

\[
YX = \frac{16 \times 88}{25} = \frac{1408}{25} = 56.32 \text{ ft}
\]

Thus, the length of \(YX\) is \(56.32\) ft.