CDS 2025 · PYQ · Triangle / Area Ratios · medium
In right triangle ABC right-angled at A with AB = 8, BC = 10, D on BC with AD ⊥ BC. What is the ratio of area of triangle ADC to area of triangle ADB?
- A.7 : 15
- B.9 : 16✓ Correct
- C.2 : 3
- D.3 : 4
BD = AB²/BC = 64/10 = 6.4. DC = AC²/BC = 36/10 = 3.6. Both triangles ADC and ADB share altitude AD, so area ratio = DC : BD = 3.6 : 6.4 = 36 : 64 = 9 : 16.
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