Analytical Geometry> The equation of base of an equilateral tr...

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?

Aryan Vartak , 7 Years ago

Grade 11

1 Answers

Arun

Last Activity: 7 Years ago

Dear Aryan

since triangle is an equilateral triangle.

we can find perpendicular height of the triangle.

height = (2 –1 – 2)/ $\small \sqrt$ 2

height = 1/ $\small \sqrt$ 2

but in an equilateral triangle height = $\small \sqrt$ 3 * a/ 2 (where a is the side)

hence

$\small \sqrt$ 3 * a/ 2 = 1/ $\small \sqrt$ 2

a = $\small \sqrt$ (2/3)

hence area = a² * (1/4) $\small \sqrt$ 3

= (2/3) * (1/4) * $\small \sqrt$ 3

= 1/2 $\small \sqrt$ 3

Regards

Arun (askIITians forum expert)

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Analytical Geometry> The equation of base of an equilateral tr...

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?

Aryan Vartak , 7 Years ago

Arun

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