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WAEC Mathematics 1993 Question 21

Question 21

Triangles and Quadrilaterals

In the diagram below, |QR| = 12cm and |QS| = 10cm. If ∠PRQ = 90°, ∠RSQ = 90° and PSQ is a straight line, find |PS|

Diagram for this question
  1. A.3.3cm
  2. B.4.4cm
  3. C.5cm
  4. D.5.5cm
  5. E.6.6cm
Show the answer and explanation

Answer: B (4.4cm)

Explanation

In right triangle RSQ, RS2 = 122 − 102 = 44. In a right triangle the altitude to the hypotenuse gives RS2 = PS × QS, so PS = 44/10 = 4.4 cm.