Question

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

Explanation:

Step1: Identify triangle type

Triangle \( PQR \) is right - angled at \( P \), so we can use the Pythagorean theorem. The Pythagorean theorem states that for a right - angled triangle with legs \( a \), \( b \) and hypotenuse \( c \), \( c=\sqrt{a^{2}+b^{2}} \). Here, \( a = 8 \), \( b = 8\sqrt{3} \) and \( c = QR \).

Step2: Apply Pythagorean theorem

First, calculate \( a^{2}=8^{2} = 64 \) and \( b^{2}=(8\sqrt{3})^{2}=8^{2}\times(\sqrt{3})^{2}=64\times3 = 192 \). Then, \( a^{2}+b^{2}=64 + 192=256 \). Now, \( QR=\sqrt{a^{2}+b^{2}}=\sqrt{256}=16 \).

Answer:

16 units