Home
Class 12
MATHS
An equilateral triangle ABC has its cent...

An equilateral triangle ABC has its centroid at the origin and the base BC lies along the line `x + y = 1`. Area of the equilateral `DeltaABC` is

Text Solution

Verified by Experts

In the given figure,
`l=CD=1/sqrt2`
`AC=2l=2/sqrt2`
`AD=2l=2/sqrt2`
In `triangle ADC`
`cos30^@=(AD)/(AC)+sqrt3/2=(AD)/a`
`a=(2AD)/sqrt3=sqrt6`
`Area = sqrt3/4a^2=sqrt3/4*6=3sqrt3/2sq.unit`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

ABC is an equilateral triangle whose centroid is origin and base BC is along the line 11x +60y = 122 . Then

ABC is an equilateral triangle whose centroid is origin and base BC is along the line 11x +60y = 122 . Then

ABC is an equilateral triangle whose centroid is origin and base BC is along the line 11x +60y = 122 . Then

ABC is an equilateral triangle whose centroid is origin and base BC is along the line 11x +60y = 122 . Then

An equilateral triangle has its circumcentre at origin and one of the sides is along the line x + y -1 = 0 and cordinate of vertex A is (-1,-1). Find the equations of the other two sides.

An equilateral triangle has its circumcentre at origin and one of the sides is along the line x + y -1 = 0 and cordinate of vertex A is (-1,-1). Find the equations of the other two sides.

One vertex of the equilateral triangle with centroid at the origin and one side as x+y-2=0 is

One vertex of the equilateral triangle with centroid at the origin and one side as x+y-2=0 is :