Mathematics - Properties of Triangle Question with Solution | TestHub

MathematicsProperties of TriangleLength of angle bisector and median / Dist. between sp. PointsMedium2 minQB

MathematicsMediumsingle choice

In triangle ABC, medians AD and BE are drawn. If AD=4, $∠ D A B$ = $π$ /6 and $∠ A BE$ = $π$ /3, find the area of triangle ABC.

Options:

Answer:

Solution:

The medians meet at centroid G and AG=2AD/3=8/3. Since $∠ G A B$ = $π$ /6 and $∠ A BG$ = $π$ /3, $∠ A GB$ = $π$ /2, and BG=AG cot( $π$ /3)=8/(3 $3$ ). Hence [ABC]=3[ABG]=3(AG)(BG)/2=32/(3 $3$ ).

Stream:JEESubject:MathematicsTopic:Properties of TriangleSubtopic:Length of angle bisector and median / Dist. between sp. Points

⏱ 2mℹ️ Source: QB

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