Question

Se stie ca triunghiul ADE este as3menea cu triunghiul ABC DE=10 BC=15 Aria triunghiului ABC este egala cu 90 cm².Aflați aria triunghiului ADE.Va rog ajutatima!!​

Answer 1

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Answer 2

 

$\displaystyle\bf\\\triangle ABC\sim\triangle ADE\\\\BC=15~cm\\\\DE=10~cm\\\\Raportul~de~asemanare~dintre~\triangle ABC~si~\triangle ADE~este:\\\\k=\frac{BC}{DE}=\frac{15}{10}=1,\!5\\\\\implies~Raportul~ariilor=k^2=1,\!5^2=\boxed{\bf2,\!25}\\\\\implies aria~\triangle ADE~\textbf{ este de 2,25 ori mai mica decat aria }\triangle ABC.\\\\Aria~\triangle ABC=90~cm^2\\\\Aria~\triangle ADE=\frac{Aria~\triangle ABC}{2,25}=\frac{90~cm^2}{2,25}= \boxed{\bf40~cm^2}$