Question
In a triangle PQR, S is a point on the side QR such that
PS⊥QR, then which of the following options is true?Solution
Since PS is perpendicular to QR, PS acts as the height from vertex P to the base QR in the right triangle PSQ and PSR. In △PSQ (right triangle): PQ² = PS² + QS² (by Pythagoras) In △PSR (right triangle): PR² = PS² + SR² (by Pythagoras) Adding these two equations: PQ² + PR² = (PS² + QS²) + (PS² + SR²) Simplifying: PQ² + PR² = 2PS² + QS² + SR² Since S is a point on QR: QS + SR = QR Therefore, PR² + QS² = PQ² + SR²
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