Question

find the length of \\(\overline{qv}\\) for square qrst.
the length of \\(\overline{qv}\\) is
(type an integer or decimal rounded to one decimal place as needed.)

Explanation:

Step1: Recall square diagonal properties

In a square, diagonals are equal and bisect each other. Also, the diagonal \( d \) of a square with side length \( s \) is \( d = s\sqrt{2} \). Here, side \( QR = 11 \), so diagonal \( QT \) (or \( RS \)) length is \( 11\sqrt{2} \).

Step2: Find length of \( QV \)

Since diagonals bisect each other, \( QV=\frac{1}{2}QT \). Substitute \( QT = 11\sqrt{2} \), so \( QV=\frac{11\sqrt{2}}{2} \). Calculate \( \frac{11\sqrt{2}}{2}\approx\frac{11\times1.4142}{2}\approx\frac{15.5562}{2}\approx7.8 \) (rounded to one decimal place).

Answer:

\( 7.8 \)