An extended right triangle with area comparisons

An extended right triangle with area comparisons

Secondary 2
TGM Original Questions

In \(\triangle ABD\), \(AB=9\) cm, \(AD=12\) cm and \(BD=15\) cm. Line \(AB\) is produced through \(B\) to \(C\), with \(BC=6\) cm.

  1. Show \(ABD\) is right-angled.
  2. Find \(CD\).
  3. Find area \(ABD\).
  4. Find the shortest distance from \(A\) to \(BD\).
  5. Find area \(ABD\) : area \(BCD\).

Solution:

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Answer:(a) right-angled at \(A\); (b) \(3\sqrt{41}\) cm; (c) \(54\text{ cm}^2\); (d) \(7.2\) cm; (e) \(3:2\).

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