Question

ABC is an equilateral traing such that the vertices B & C on two parallel lines at a distance 6 If A lies between the parallel lines at a distance 4 from one of them then the length of a side of the equilateral triangle is

• A. 8
• B. $\sqrt{\frac{88}{3}}$
• C. $\frac{4\sqrt{7}}{\sqrt{3}}$
• D. None

Answer 1

Answer: (C)

$\frac{4\sqrt{7}}{\sqrt{3}}$

Answer 2

DABD cos q = $\frac{2}{a}$ …(1)

DAEC cos (120⁰ – q) = $\frac{4}{a}$ …(2)

cos 120⁰ cosq + sin120⁰ sinq = $\frac{4}{a}$

– $\frac{1}{2}$ cos q + $\frac{\sqrt{3}}{2}$sinq = $\frac{4}{a}$

$\frac{\sqrt{3}}{2}$sin q = $\frac{4}{a} + \frac{1}{2} \times \frac{2}{a}$̃ $\frac{\sqrt{3}}{2}\sin\theta = \frac{5}{a}$

$\frac{3}{4}$ (1 – cos² q) = $\frac{25}{a^{2}}$

$\frac{3}{4}\left( 1 - \frac{4}{a^{2}} \right) = \frac{25}{a^{2}}$ ̃ $\frac{3}{4} = \frac{25}{a^{2}} + \frac{3}{a^{2}}$

a² = $\frac{28 \times 4}{3}$ ̃ a = $\frac{4\sqrt{7}}{\sqrt{3}}$