Multiple choice

∆PQR is inscribed in the circle whose radius is 14 cm. If PQ is the diameter of the circle and PR = 10 cm, then find the area of the ∆PQR?

  1. 196

  2. 30√19

  3. 40√17

  4. 35√21
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Since PQ is the diameter, ∠PRQ = 90° (angle in semicircle). Using Pythagoras: PQ² = PR² + QR². PQ = diameter = 2 × 14 = 28 cm. PR = 10 cm. QR² = 28² - 10² = 784 - 100 = 684, so QR = √684 = 6√19 cm. Area of right triangle PQR = 1/2 × base × height = 1/2 × 10 × 6√19 = 30√19 cm².

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