in a triangle ABC, BE= 2EC and its area is 60 cm²​,then find the area of triangle AEC.
 

Dear Student,

Please find below the solution to the asked query :

$$\begin{gathered} \mathrm{Using} \mathrm{the} \mathrm{property} \mathrm{that} \mathrm{the} \mathrm{ratio} \mathrm{in} \mathrm{which} \mathrm{point} \mathrm{E} \mathrm{is} \mathrm{dividing} \mathrm{the} \mathrm{line} \mathrm{BC} \\ \mathrm{will} \mathrm{be} \mathrm{same} \mathrm{as} \mathrm{the} \mathrm{ratio} \mathrm{in} \mathrm{which} \mathrm{AE} \mathrm{will} \mathrm{divide} \mathrm{the} \mathrm{area} \mathrm{of} \mathrm{triangle} \mathrm{ABC}. \\ \mathrm{So} \\ \mathrm{Area} \mathrm{of} \mathrm{triangle} \mathrm{AEC}=\frac{1}{1+2}\times \mathrm{Area} \mathrm{of} \mathrm{triangle} \mathrm{ABC} \\ =\frac{1}{3}\times 60= 20 {\mathrm{cm}}^2 \end{gathered}$$

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