Question

consider triangle pqr. what is the length of side qr? 8 units 8√3 units 16 units 16√3 units

Explanation:

Step1: Recall Pythagorean theorem

In a right - triangle, for sides \(a\), \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Here, in right - triangle \(PQR\) with \(\angle P = 90^{\circ}\), \(PQ = 8\sqrt{3}\) and \(PR = 8\), and we want to find \(QR\) (the hypotenuse).

Step2: Apply the formula

Let \(a=8\sqrt{3}\), \(b = 8\). Then \(QR^{2}=(8\sqrt{3})^{2}+8^{2}\).
First, calculate \((8\sqrt{3})^{2}=8^{2}\times(\sqrt{3})^{2}=64\times3 = 192\) and \(8^{2}=64\).
So \(QR^{2}=192 + 64=256\).

Step3: Solve for \(QR\)

Take the square root of both sides: \(QR=\sqrt{256}=16\).

Answer:

C. 16 units