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Question Number 144074 by bobhans last updated on 21/Jun/21

$$\mathrm{The}\mathrm{parallelogram}\mathrm{ABCD}\mathrm{has}$$ $$\mid \mid \mathrm{AB}\mid \mid =6,\mid \mid \mathrm{AC}\mid \mid =7\mathrm{\&}\mathrm{d}(\mathrm{D},\mathrm{AC})=2$$ $$\mathrm{Find}\mathrm{d}(\mathrm{D},\mathrm{AB}).$$

Answered by liberty last updated on 21/Jun/21

$${\mathrm{Area}}_{\mathrm{\Delta }\mathrm{ADC}}=\frac{2\times 7}{2}=7$$ $${\mathrm{Area}}_{◻\mathrm{ABCD}}=2\times \left[{\mathrm{area}}_{\mathrm{\Delta }\mathrm{ADC}}\right]=14$$ $${\mathrm{Area}}_{◻\mathrm{ABCD}}=\mathrm{AB}\times \mathrm{DF}=14$$ $$\mid \mid \mathrm{DF}\mid \mid =\frac{14}{6}=\frac{7}{3}.$$

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