If `x` is the length of a median of an equilateral triangle, then its area is (a) `x^2` (b) `1/2x^2` (c) `(sqrt(3))/2\ x^2` (d) `(sqrt(3))/3\ x^2`

The equation of the base of an equilateral triangle ABC is x+y=2 and the vertex is (2,-1). The area of the triangle ABC is: (sqrt(2))/(6) (b) (sqrt(3))/(6) (c) (sqrt(3))/(8) (d) None of these

P is a point on the line y+2x=1, and Q and R two points on the line 3y+6x=6 such that triangle PQR is an equilateral triangle.The length of the side of the triangle is (2)/(sqrt(5)) (b) (3)/(sqrt(5))(c)(4)/(sqrt(5))(d) none of these

The equation of the circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3a is: a x^(2)+y^(2)=9a^(2) b) x^(2)+y^(2)=16a^(2) c) x^(2)+y^(2)=4a^(2) d) x^(2)+y^(2)=a^(2)

If cos^-1(sqrt3x) and cos^-1 xare two angles of a right angled triangle, then x= (A) 1/sqrt(6) (B) 0 (C) sqrt(3)/2 (D) 1/2

Let g(x) be a function defined on [-1,1] .If the area of the equilateral triangle with two of its vertices at (0,0) a n d(x,g(x)) is (a) (sqrt(3))/(4) then the function g(x) is (b) g(x)=+-sqrt(1-x^(2))(cx)=sqrt(1-x^(2))(d)g(x)=-sqrt(1-x^(2))g(x)=sqrt(1+x^(2))(d)

If area of an equilateral triangle inscribed in the circle x^(2)+y^(2)+10x+12y+c=0 is 27sqrt(3), then the value of c is (a) 25(b)-25 (c) 36(d)-36

A rectangle is inscribed in an equilateral triangle of side length 2a units.The maximum area of this rectangle can be sqrt(3)a^(2)(b)(sqrt(3)a^(2))/(4)a^(2)(d)(sqrt(3)a^(2))/(2)

If the equation of base of an equilateral triangle is 2x-y=1 and the vertex is (-1,2), then the length of the sides of the triangle is sqrt((20)/(3)) (b) (2)/(sqrt(15))sqrt((8)/(15)) (d) sqrt((15)/(2))

If mean value theorem holds good for the function f(x)=(x-1)/(x) on the interval [1,3] then the value of 'c' is 2 (b) (1)/(sqrt(3))( c) (2)/(sqrt(3))(d)sqrt(3)