What is ratio of area of triangle ADC to area of triangle ADB ?

Consider the following for the next two (02) items that follow :<br>ABC is a triangle right-angled at A. Further, AB=8 cm, BC=10 cm. D is the point on BC such that AD is perpendicular to BC.

  1. A. 7:15
  2. B. 9:16
  3. C. 2:3
  4. D. 3:4

Correct Answer: B. 9:16

Explanation

By Pythagoras, AC = 6 cm. The areas of \triangle ADC and \triangle ADB sharing the same height AD are proportional to their bases CD and DB. For a right triangle, AC^2 = CD \times BC and AB^2 = DB \times BC. The ratio \frac{CD}{DB} = \frac{AC^2}{AB^2} = \frac{36}{64} = \frac{9}{16}.

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