AP EAMCET · Maths · Straight Lines
If the equation of the base of an equilateral triangle is \(x+y=6\) and the opposite vertex is the point \((-1,-1)\) then the area of the triangle is equal to sq. units
- A \(\frac{8}{\sqrt{3}}\)
- B \(32 \sqrt{3}\)
- C \(\frac{32}{\sqrt{3}}\)
- D \(16 \sqrt{3}\)
Answer & Solution
Correct Answer
(C) \(\frac{32}{\sqrt{3}}\)
Step-by-step Solution
Detailed explanation
\(h = \frac{|Ax_0 + By_0 + C|}{\sqrt{A^2 + B^2}}\) \(h = \frac{|1(-1) + 1(-1) - 6|}{\sqrt{1^2 + 1^2}} = \frac{|-8|}{\sqrt{2}} = \frac{8}{\sqrt{2}} = 4\sqrt{2}\) \(a = \frac{2h}{\sqrt{3}}\) \(a = \frac{2(4\sqrt{2})}{\sqrt{3}} = \frac{8\sqrt{2}}{\sqrt{3}}\)…
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