Exams › SSC CGL (Prelims) › General

In triangle PQR, S is a point on side QR such that PS is perpendicular to QR. Which of the following relations is necessarily true?

1. PS^2 + QS^2 = PQ^2 + PR^2
2. PS^2 + PR^2 = PQ^2 + QR^2
3. PQ^2 + PR^2 = QS^2 + SR^2
4. PR^2 + QS^2 = PQ^2 + SR^2

Correct answer: PR^2 + QS^2 = PQ^2 + SR^2

Solution

Since PS perpendicular QR: PQ^2 = PS^2 + QS^2 and PR^2 = PS^2 + SR^2. Subtracting: PR^2 - PQ^2 = SR^2 - QS^2, which rearranges to PR^2 + QS^2 = PQ^2 + SR^2.

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