A right triangle is drawn in a semicircle of radius `1/2` with one of its legs along the diameter. If the maximum area of the triangle is `M` , then the value of `32sqrt(3)M ` is______

The area of the triangle inscribed in a circle of radius 4 and the ratio of its angles in the ratio 5:4:3 is

The area of a right triangle is 6864 sq. units. If the ratio of its legs is 143 : 24 , then the value of r is ______

The base of a triangle is 18m more than the double of its height. If the area of the triangle be 360 sq-m, then find the height of the triangle.

From the point (-1,2), tangent lines are to the parabola y^(2)=4x . If the area of the triangle formed by the chord of contact and the tangents is A, then the value of A//sqrt(2) is ___________ .

Find the area of the triangle with vertices at (-4,1),(1,2),(4,-3).

In a ΔABC, a semicircle is inscribed, whose diameter lies on the side c. Then find the radius of the semicircle.(Where Δ is the area of the triangle ABC)

Let a and b represent the lengths of a right triangles legs. If d is the diameter of a circle inscribed into the triangle, and D is the diameter of a circle circumscribed on the triangle, the d+D equals. (a) a+b (b) 2(a+b) (c) 1/2(a+b) (d) sqrt(a^2+b^2)

The maximum area of the triangle whose sides a,b and c satisfy 0leqaleq1,1leqbleq2 and 2leqcleq3 is

The length of the hypotenuse of a right angled triangle is a Find the lenghts of its other sides , so that the area of the triangle is maximum.

Two medians drawn from the acute angles of a right angled triangle intersect at an angle pi/6. If the length of the hypotenuse of the triangle is 3 units, then the area of the triangle (in sq. units) is (a) sqrt3 (b) 3 (c) sqrt2 (d) 9