Question

Triangle PQR is similar to triangle XYZ.

What is the length of line segment XZ?
25 points

Answer 1

16

Explanation:

Answer 2

The length of line segment XZ in triangle PQR, given PQ =
`4` in, QR =
`6` in, and PR =
`9` in, is
`13.5` inches based on similarity ratios.

In similar triangles, corresponding sides are proportional. The ratio of corresponding sides in similar triangles is equal. For triangles PQR and XYZ:

`\[ (PQ)/(XY) = (QR)/(YZ) = (PR)/(XZ) \]`

Given that
`\(PQ = 4\)` in,
`\(QR = 6\)` in,
`\(PR = 9\)` in,
`\(XY = 6\)` in, and
`\(YZ = 9\)` in:

`\[ (4)/(6) = (6)/(9) = (9)/(XZ) \]`

Simplify the ratios:

`\[ (2)/(3) = (2)/(3) = (9)/(XZ) \]`

Now, solve for XZ:

`XZ = 3 * 9 /2 = 27 / 2 = 13.5`

Therefore, the length of line segment XZ is
`13.5` inches.