Coordinates of the vertices A,B,C of a triangle ABC are (m+3,m),(m,m-2)and (m+2,m+2) respectively Show that the area of the triangle ABC is independent of m .

The coordinates of the vertices of a triangle are [m(m+1),m+1],[(m+1)(m+2),m+2] and[(m+2)(m+3), m+3], show that the area of the triangle is independent of m

The sides of a triangle are 11 m, 55 m and 50 m respectively. Find the area of the triangle.

Find the area of a triangle ABC whose sides are 9m ,12 m a n d15 m respectively.

Find the area of a triangle ABC whose sides are 9m,12 mand15m respectively.

Three particles of masses m , m and 4kg are kept at a verticals of triangle ABC . Coordinates of A , B and C are (1,2) , (3,2) and (-2,-2) respectively such that the centre of mass lies at origin. Find the value of mass m . Hint. x_(cm)=(sum_(i-1)^(3)m_(i)x_(i))/(sum_(i=1)^(3)m_(i)) , y_(cm)=(sum_(i=1)^(3)m_(i)y_(i))/(sum_(i=1)^(3)m_(i))

Three particles of masses m , m and 4kg are kept at a verticals of triangle ABC . Coordinates of A , B and C are (1,2) , (3,2) and (-2,-2) respectively such that the centre of mass lies at origin. Find the value of mass m . Hint. x_(cm)=(sum_(i-1)^(3)m_(i)x_(i))/(sum_(i=1)^(3)m_(i)) , y_(cm)=(sum_(i=1)^(3)m_(i)y_(i))/(sum_(i=1)^(3)m_(i))

Three particles of masses m , m and 4kg are kept at a verticals of triangle ABC . Coordinates of A , B and C are (1,2) , (3,2) and (-2,-2) respectively such that the centre of mass lies at origin. Find the value of mass m . Hint. x_(cm)=(sum_(i-1)^(3)m_(i)x_(i))/(sum_(i=1)^(3)m_(i)) , y_(cm)=(sum_(i=1)^(3)m_(i)y_(i))/(sum_(i=1)^(3)m_(i))

The areas of two similar triangles are 9\ c m^2 and 16\ c m^2 respectively . The ratio of their corresponding sides is

(b) The two sides of a triangle are 68 m and 75 m and its semi-perimeter is 110 m. Then find the area of the triangle.

If the length of medians A A_(1),BB_(1) and C C_(1) of triangle ABC are m_(a),m_(b) and m_(c) respectively, then: