Distances in a parallelogram

Distances in a parallelogram

Secondary 2
8 marks
TGM Original Questions

Parallelogram \(PQRS\) has area \(72\text{ cm}^2\), \(SP=10\) cm and \(PQ=12\) cm. The perpendicular from \(S\) meets \(PQ\) at \(T\). Find

Point \(T\) lies on the segment \(PQ\).

  1. \(ST\),[2]
  2. \(PT\),[2]
  3. \(SQ\),[2]
  4. the shortest distance from \(P\) to \(QS\).[2]

Solution:

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Answer:(a) \(6\) cm (b) \(8\) cm (c) \(2\sqrt{13}\approx7.21\) cm (d) \(36/\sqrt{13}\approx9.98\) cm.

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