Question

question 10 (multiple choice worth 1 points) (05.01r mc) in △rst, what is the length of segment rt? 18 72 36√3 36√2

Explanation:

Step1: Determine the type of triangle

Since \(\angle R = 45^{\circ}\) and \(\angle T=45^{\circ}\), \(\triangle RST\) is a \(45 - 45-90\) right - triangle. In a \(45 - 45-90\) triangle, the legs are equal (\(RS = ST\)) and the hypotenuse \(RT\) is related to the leg \(x\) (here \(x = 36\)) by the formula \(RT=\sqrt{2}x\).

Step2: Calculate the length of \(RT\)

Substitute \(x = 36\) into the formula \(RT=\sqrt{2}x\). So \(RT = 36\sqrt{2}\).

Answer:

\(36\sqrt{2}\)