Question

1. qr = _ sr = _ sq = _ pr = _ qt = _

Explanation:

Step1: Use the property of rectangle

In rectangle \(PQRS\), \(PQ = SR\), \(PS=QR\), and the diagonals \(SQ = PR\), and \(QT=\frac{1}{2}SQ\). Given \(PQ = 24\), \(PS = 10\).
Since \(PQRS\) is a rectangle, \(QR=PS = 10\) (opposite sides of a rectangle are equal).

Step2: Find \(SR\)

\(SR = PQ=24\) (opposite sides of a rectangle are equal).

Step3: Use the Pythagorean theorem to find the diagonal

In right - triangle \(SPQ\), by the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 10\), \(b = 24\), and \(c=SQ\) (or \(PR\)).

$$SQ=\sqrt{10^{2}+24^{2}}=\sqrt{100 + 576}=\sqrt{676}=26$$

Since \(SQ = PR\) (diagonals of a rectangle are equal), \(PR = 26\).

Step4: Find \(QT\)

Since the diagonals of a rectangle bisect each other, \(QT=\frac{1}{2}SQ\). Given \(SQ = 26\), then \(QT=\frac{26}{2}=13\).

Answer:

\(QR = 10\), \(SR = 24\), \(SQ = 26\), \(PR = 26\), \(QT = 13\)