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BITSAT 2016

Exam: BITSAT
Year: 2016
Subject: Mathematics
Chapter: Properties of Triangles

BITSAT 2016 · Mathematics · Properties of Triangles

In a ABC, if A a = B b = C c , and the side a=2, then area of the...

In a

\triangle \mathrm{ABC},

if

\frac{\cos A}{\mathrm{a}}=\frac{\cos \mathrm{B}}{\mathrm{b}}=\frac{\cos \mathrm{C}}{\mathrm{c}},

and the side

\mathrm{a}=2,

then area of the triangle is

Options

A1
B2
C $\frac{\sqrt{3}}{2}$
D $\sqrt{3}$

Correct answer

D. $\sqrt{3}$

Step-by-step solution

\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}\Rightarrow \frac{\cos \mathrm{A}}{2 \mathrm{R} \sin \mathrm{A}}=\frac{\cos \mathrm{B}}{2 \mathrm{R} \sin \mathrm{B}}=\frac{\cos \mathrm{C}}{2 \mathrm{R} \sin \mathrm{C}}\Rightarrow \cot A=\cot B=\cot C\Rightarrow

\mathrm{A}=\mathrm{B}

=\mathrm{C}=60^{{}^{\circ}} \Rightarrow \Delta \mathrm{ABC}

is equilateral Hence, area of

\Delta=\frac{\sqrt{3}}{4} \mathrma^{2}=\sqrt{3}

.

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