Question

If triangle XYZ is similar to triangle AYB, and YB = 15 ft, YA = 9 ft, and YZ = 63 ft, then what is the length of YX?

Answer 1

Since triangles XYZ and AYB are similar, their corresponding sides are proportional. This means that the ratios of the lengths of corresponding sides are equal.

Given the following lengths:
- YB = 15 ft
- YA = 9 ft
- YZ = 63 ft

We want to find the length of YX.

Since the triangles are similar, we can set up a ratio using the corresponding sides:
\[
\frac{YB}{YA} = \frac{YZ}{YX}
\]

Substituting the known values:
\[
\frac{15}{9} = \frac{63}{YX}
\]

Next, we can simplify the left side of the equation:
\[
\frac{15}{9} = \frac{5}{3}
\]

Now we have:
\[
\frac{5}{3} = \frac{63}{YX}
\]

To find YX, we can cross-multiply:
\[
5 \cdot YX = 3 \cdot 63
\]

Calculating the right-hand side:
\[
3 \cdot 63 = 189
\]

Now we have:
\[
5 \cdot YX = 189
\]

To solve for YX, divide both sides by 5:
\[
YX = \frac{189}{5} = 37.8 \text{ ft}
\]

Thus, the length of YX is:
\[
\boxed{37.8 \text{ ft}}
\]