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SSC CHSL 2020 · PYQ · Geometry - Triangle · medium

PQR is an isosceles triangle such that PQ = QR = 10 cm and ∠PQR = 90°. What is the length of the perpendicular drawn from Q on PR?

  1. A.4√2 cm
  2. B.5√2 cm✓ Correct
  3. C.6√2 cm
  4. D.7√2 cm

Explanation

PR = √(PQ²+QR²) = √(100+100) = 10√2. Area of △PQR = (1/2)×10×10 = 50. Also Area = (1/2)×PR×h = (1/2)×10√2×h. So h = 100/(10√2) = 10/√2 = 5√2 cm.
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