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 c` is______

An equilateral triangle is drawn on a diagonal of a square of perimeter 16cm . If the area of triangle is xsqrt3 cm^2 , then the value of x is

A small card is in the shape of an isosceles triangle with a semicircle on its base. If the diameter of the semicircle is 6 cm, and the hright of the triangle is 3 cm, find the area of the card.

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 three sides of a trapezium are equal each being 6 cms long. Let Delta cm^(2) be the maximum area of the trapezium. The value of sqrt(3) Delta is :

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

Consider a right triangle with legs of length a and b and hypotenuse of length c . If k denotes the area of the triangle then the value of (a+b) equals

The base and the height of a triangle are in the ratio 5:3. If the area of the triangle is 67.5 m^(2) , find its base and height.

The lengths of the two shorter legs of a right triangle add up to 40 units. What is the maximum possible area of the triangle?

In the right triangle BAC, angle A=pi/2 and a+b=8 . The area of the triangle is maximum when angle C , is