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The equation of base of an equilateral triangle is "x + y = 2". If the vertex is (2, -1), then the area of the triangle is?

The equation of base of an equilateral triangle is "x + y = 2". If the vertex is (2, -1), then the area of the triangle is?

Grade:11

1 Answers

Arun
25750 Points
6 years ago
Dear Aryan
 
since triangle is an equilateral triangle.
we can find perpendicular height of the triangle.
height = (2 –1 – 2)/\small \sqrt2
height = 1/\small \sqrt2
 
but in an equilateral triangle height  = \small \sqrt3 * a/ 2    (where a is the side)
hence
\small \sqrt3 * a/ 2 = 1/\small \sqrt2
a = \small \sqrt(2/3)
hence area  =  a2 * (1/4)\small \sqrt3
 = (2/3) * (1/4) * \small \sqrt3
 = 1/2\small \sqrt3
 
Regards
Arun (askIITians forum expert)

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