In a - ABC - A -2 -3- b - c -3 -3 cm and Area - ABC -9 -3-2 cm 2 then a isA- 6 -3 cmB- 9 cmC- 18 cmD- None of then

The correct option is B 9 cm 1 2bc sin2π 3=9√(3) 2 or 1 2π 2.b c=9√(3) 2 ⇒ bc=18 Also cos2π 3=b^2+c^2 a^2/2bc ⇒ 1 2=(b c)^2+2bc a^2/2bc or (b c)^2+3bc a^2=0 ...

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Standard XII

Mathematics

Cosine Rule

In a Δ ABC , ...

Question

In a $Δ A B C, A = \frac{2 π}{3}, b - c = 3 \sqrt{3}$ cm and Area $(Δ A B C)$ $= \frac{9 \sqrt{3}}{2} c m^{2}$ then a is

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9 cm

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18cm

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None of then

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Solution

The correct option is B
9 cm

$\frac{1}{2} b c s i n \frac{2 π}{3} = \frac{9 \sqrt{3}}{2} o r \frac{1}{2} \frac{π}{2} . b c = \frac{9 \sqrt{3}}{2}$
$\Rightarrow b c = 18$
Also $c o s \frac{2 π}{3} = \frac{b^{2} + c^{2} - a^{2}}{2 b c} \Rightarrow - \frac{1}{2} = \frac{(b - c)^{2} + 2 b c - a^{2}}{2 b c}$
or $(b - c)^{2} + 3 b c - a^{2} = 0 o r 27 + 54 = a^{2} o r a^{2} = 81$
$\Rightarrow a = 9$ cm

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