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प्रश्न
In ∆ABC, B – D – C and BD = 7, BC = 20 then Find following ratio.
\[\frac{A\left( ∆ ADC \right)}{A\left( ∆ ABC \right)}\]
उत्तर
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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In the figure, PQ ⊥ BC, AD ⊥ BC. To find the ratio of A(ΔPQB) and A(ΔPBC), complete the following activity.
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Now, A(ΔPQB) = `1/2 xx square xx square`
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Therefore,
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= `square/square`
