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Question
In ∆ABC, B – D – C and BD = 7, BC = 20 then Find following ratio.
\[\frac{A\left( ∆ ADC \right)}{A\left( ∆ ABC \right)}\]
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Solution
Construction: Draw a perpendicular from vertex A to line BC.
\[\frac{A\left( ∆ ADC \right)}{A\left( ∆ ABC \right)} = \frac{\frac{1}{2} \times AX \times DC}{\frac{1}{2} \times AX \times BC}\]
\[ = \frac{DC}{BC}\]
\[ = \frac{13}{20} \left( \because DC = BC - BD \right)\]
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