Question

select the correct answer.
in rectangle ( pqrs ), ( pq = 18 ), ( ps = 14 ), and ( pr = 22.8 ). diagonals ( overline{pr} ) and ( overline{qs} ) intersect at point ( t ). what is the length of ( overline{tq} )?
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 \(QS = 22.8\) into the formula, we get \(TQ=\frac{1}{2}\times22.8\).

Step3: Calculate the value of \(TQ\)

\(TQ=\frac{22.8}{2}=11.4\)

Answer:

C. 11.4