Question and Answers Forum

All Questions      Topic List

Mensuration Questions

Previous in All Question      Next in All Question      

Previous in Mensuration      Next in Mensuration      

Question Number 177046 by Ar Brandon last updated on 30/Sep/22

Answered by som(math1967) last updated on 30/Sep/22

Area(△ADE+△BEC)=(1/2)AreaABCD =(x/2) (let) Area△AEB=(1/2)ABCD=(x/2) Area(ADEP+△ADE) =△BEC+△ADE=(x/2) area△APE=Area(ADEP+△ADE) =(x/2) ∴ar△APE=ar△AEB ⇒((ar△APE)/(ar△AEB))=(1/1) ⇒((PE)/(EB))=(1/1)

$${Area}\left(\bigtriangleup{ADE}+\bigtriangleup{BEC}\right)=\frac{\mathrm{1}}{\mathrm{2}}{AreaABCD} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{{x}}{\mathrm{2}}\:\left({let}\right) \\ $$$${Area}\bigtriangleup{AEB}=\frac{\mathrm{1}}{\mathrm{2}}{ABCD}=\frac{{x}}{\mathrm{2}} \\ $$$${Area}\left({ADEP}+\bigtriangleup{ADE}\right) \\ $$$$=\bigtriangleup{BEC}+\bigtriangleup{ADE}=\frac{{x}}{\mathrm{2}} \\ $$$$\:{area}\bigtriangleup{APE}={Area}\left({ADEP}+\bigtriangleup{ADE}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:=\frac{{x}}{\mathrm{2}} \\ $$$$\therefore{ar}\bigtriangleup{APE}={ar}\bigtriangleup{AEB} \\ $$$$\Rightarrow\frac{{ar}\bigtriangleup{APE}}{{ar}\bigtriangleup{AEB}}=\frac{\mathrm{1}}{\mathrm{1}} \\ $$$$\Rightarrow\frac{{PE}}{{EB}}=\frac{\mathrm{1}}{\mathrm{1}} \\ $$$$ \\ $$

Commented by som(math1967) last updated on 30/Sep/22

Commented by Ar Brandon last updated on 30/Sep/22

Thank you Sir

Terms of Service

Privacy Policy

Contact: info@tinkutara.com