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JEE Main 2003

Exam: JEE Main
Year: 2003
Subject: Mathematics
Chapter: Properties of Triangles

JEE Main 2003 · Mathematics · Properties of Triangles

In a triangle ABC , medians AD and BE are drawn. If AD=4,...

In a triangle

\mathrm{ABC}

, medians

\mathrm{AD}

and

\mathrm{BE}

are drawn. If

\mathrm{AD}=4, \angle \mathrm{DAB}=\frac{\pi}{6}

and

\angle \mathrm{ABE}=\frac{\pi}{3}

, then the area of the

\triangle \mathrm{ABC}

is

In a triangle ABC , medians AD and BE are drawn. If AD=4, DAB=(π)/(6) and ABE=(π)/(3) , then the area of the ABC is

In a triangle ABC , medians AD and BE are drawn. If AD=4, DAB=(π)/(6) and ABE=(π)/(3) , then the area of the ABC is

Options

A $\frac{64}{3}$
B $\frac{8}{3}$
C $\frac{16}{3}$
DNone of these

Correct answer

D. None of these

Step-by-step solution

In a triangle ABC , medians AD and BE are drawn. If AD=4, DAB=(π)/(6) and ABE=(π)/(3) , then the area of the ABC is

\tan 60^{\circ}=\frac{8 / 3}{x}

or

x=\frac{8}{3 \sqrt{3}}

In a triangle ABC , medians AD and BE are drawn. If AD=4, DAB=(π)/(6) and ABE=(π)/(3) , then the area of the ABC is

Area of

\triangle \mathrm{ABD}=\frac{1}{2} \times 4 \times \frac{8}{3 \sqrt{3}}=\frac{16}{3 \sqrt{3}}

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