Question

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

Explanation:

Step1: Identify triangle type

In square QRST, \( \triangle QRT \) is a right triangle with legs \( QR = QT = 17 \) (sides of square) and hypotenuse \( RT \).

Step2: Apply Pythagorean theorem

The Pythagorean theorem states \( c = \sqrt{a^2 + b^2} \), where \( a = 17 \), \( b = 17 \), and \( c = RT \).
Substitute values: \( RT = \sqrt{17^2 + 17^2} = \sqrt{2 \times 17^2} = 17\sqrt{2} \).
Calculate \( 17\sqrt{2} \approx 17 \times 1.414 \approx 24.0 \) (rounded to one decimal place).

Answer:

24.0