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Question Number 70592 by behi83417@gmail.com last updated on 05/Oct/19

Commented by behi83417@gmail.com last updated on 05/Oct/19

$$\mathrm{convex}\mathrm{ABCD},\mathrm{is}\mathrm{given}\mathrm{with}:$$$$\mathrm{S}\left(\mathrm{DCE}\right)=9,\mathrm{S}\left(\mathrm{CBE}\right)=10,\mathrm{S}\left(\mathrm{BAE}\right)=13.$$$$\Rightarrow \mathrm{S}\left(\mathrm{ADE}\right)=?$$

Answered by mr W last updated on 06/Oct/19

Commented by mr W last updated on 06/Oct/19

$$S_1=\frac{dc}{2}=9$$$$S_2=\frac{bc}{2}=10$$$$S_3=\frac{ba}{2}=13$$$$S_4=\frac{da}{2}=?$$$$S_1{S}_3=\frac{dcba}{4}=\frac{abcd}{4}$$$$S_2{S}_4=\frac{bcda}{4}=\frac{abcd}{4}$$$$\Rightarrow S_1{S}_3=S_2{S}_4$$$$\Rightarrow S_4=\frac{S_1{S}_3}{S_2}=\frac{9\times 13}{10}=11.7$$

Commented by behi83417@gmail.com last updated on 06/Oct/19

$$\mathrm{nice}\mathrm{solution}\mathrm{dear}\mathrm{master}.\mathrm{thanks}\mathrm{in}$$$$\mathrm{advance}\mathrm{sir}.$$

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