CAT 2021 Slot 2 · Quant · Question 11
CAT 2021 Slot 2 previous year question on Triangles, with the answer and a step-by-step solution.
Answer & solution
Answer: 30
Triangles ADE and ABC share the angle at A, so their areas are in the ratio of the products of the sides enclosing that angle:
\frac{\left[ ADE \right]}{\left[ ABC \right]}=\frac{AD}{AB}\times \frac{AE}{AC}.
From AD : BD =2:1 we get \frac{AD}{AB}=\frac{2}{3}, and from AE : CE =2:3 we get \frac{AE}{AC}=\frac{2}{5}.
So \frac{\left[ ADE \right]}{\left[ ABC \right]}=\frac{2}{3}\times \frac{2}{5}=\frac{4}{15}, and \left[ ABC \right]=8\times \frac{15}{4}=30 sq cm.
The common trap is to use \frac{AD}{BD} and \frac{AE}{CE} instead of the ratios to the full sides.
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