AP EAMCET · Maths · Straight Lines
The equation of the base of an equilateral triangle is \(x+y=2\) and its opposite vertex is \((2,1)\). If \(m_1, m_2\) are the slopes of the other two sides and the length of its side is a, then \(\left|m_1-m_2\right|+a \sqrt{2}=\)
- A \(8 \sqrt{3}\)
- B \(\frac{8}{\sqrt{3}}\)
- C \(4 \sqrt{\frac{2}{3}}\)
- D \(8 \sqrt{\frac{2}{3}}\)
Answer & Solution
Correct Answer
(B) \(\frac{8}{\sqrt{3}}\)
Step-by-step Solution
Detailed explanation
\(h = \frac{|1(2)+1(1)-2|}{\sqrt{1^2+1^2}} = \frac{1}{\sqrt{2}}\) \(a = \frac{2h}{\sqrt{3}} = \frac{2(1/\sqrt{2})}{\sqrt{3}} = \frac{\sqrt{2}}{\sqrt{3}}\) \(\tan 60^\circ = \left|\frac{m - (-1)}{1 + m(-1)}\right| \implies \sqrt{3} = \left|\frac{m+1}{1-m}\right|\)…
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