Question

14 rectangle pqsr and its diagonals are shown below. diagonals \\( \overline { p s } \\) and \\( \overline { q r } \\) intersect at point i. if \\( p i = 17 \\) inches, what is qr? qr = inches

Explanation:

Step1: Recall the property of rectangle diagonals

In a rectangle, the diagonals are equal and bisect each other. So \( PS = QR \) and \( PI=\frac{1}{2}PS \).

Step2: Calculate the length of \( PS \)

Given \( PI = 17\) inches. Since \( PS = 2\times PI\), then \( PS=2\times17 = 34\) inches.

Step3: Find the length of \( QR \)

Because \( PS = QR\) (diagonals of a rectangle are equal), so \( QR = 34\) inches.

Answer:

\(34\)