Question

select the correct answer.
in rectangle pqrs, pq = 18, ps = 14, and pr = 22.8. diagonals \\( \overline { p r } \\) and \\( \overline { q s } \\) intersect at point t. what is the length of \\( \overline { t q } \\)?
a. 7
b. 9
c. 11.4
d. 22.8

Explanation:

Step1: Recall the property of rectangle diagonals

In a rectangle, the diagonals are equal and bisect each other. So \(PR = QS\) and \(TQ=\frac{1}{2}QS\).

Step2: Use the given diagonal length

Since \(PR = 22.8\) and \(QS=PR\) (diagonals of a rectangle are equal), then \(TQ=\frac{1}{2}QS\). Substituting \(QS = 22.8\), we get \(TQ=\frac{22.8}{2}\).

Answer:

C. \(11.4\)