Question

question 1 (multiple choice worth 1 points) (05.01r mc) in △pqr, what is the length of segment qr? 22√3 11 11√2 22√2

Explanation:

Step1: Identify the type of triangle

Since \(\angle Q = 90^{\circ}\), \(\angle P=45^{\circ}\), \(\angle R = 45^{\circ}\), \(\triangle PQR\) is a \(45 - 45-90\) right - triangle. In a \(45 - 45-90\) triangle, the ratio of the sides is \(1:1:\sqrt{2}\), where the hypotenuse \(c\) is related to the legs \(a\) and \(b\) ( \(a = b\)) by the formula \(c=a\sqrt{2}\).

Step2: Let \(QR=x\)

Given the hypotenuse \(PR = 22\). Using the formula \(c=a\sqrt{2}\) (where \(c = PR\) and \(a=QR\)), we have \(22=x\sqrt{2}\).

Step3: Solve for \(x\)

$$x=\frac{22}{\sqrt{2}}=\frac{22\sqrt{2}}{2}=11\sqrt{2}$$

Answer:

\(11\sqrt{2}\)