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WAEC Mathematics 2012 Question 19

Question 19

Triangles and Quadrilaterals

In ΔXYZ, |XY| = 8cm, |YZ| = 10 cm and |XZ| = 6 cm. Which of these relations is true?

  1. A.|XY| + |YZ| = |XZ|
  2. B.|XY| − |YZ| = |XZ|
  3. C.|XZ|2 = |YZ|2 − |XY|2
  4. D.|YZ|2 = |XZ|2 − |XY|2
Show the answer and explanation

Answer: C (|XZ|2 = |YZ|2 − |XY|2)

Explanation

62 + 82 = 100 = 102, so |XZ|2 + |XY|2 = |YZ|2, i.e. |XZ|2 = |YZ|2 − |XY|2.