Find the volume of the largest square (maximum area) that can be formed inside a triangle having side 3, 4, 5 such that one side of the square lies on the hypotenuse of the triangle.

The ratio of the area of a square of side a and that of an equilateral triangle of side a, is

Fill in the balnks : (i) In a right triangle, the square of the hypotenuse is equal to the……….of the square of the other two sides. (ii) If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is......... (iii) Of all the line segments that can be drawn to a given line form a given point outside it, the.............is the shortest.

The number of triangles that can be formed form a regular polygon of 2n + 1 sides such that the centre of the polygon lies inside the triangle is

The number of triangles that can be formed form a regular polygon of 2n + 1 sides such that the centre of the polygon lies inside the triangle is

In a right angled triangle, square on the hypotenuse is equal to sum of the squares on the other sides. Prove the statement.

In a right angled triangle , square on the hypotenuse is equal to sum of the squares on the other sides. Prove the statement.

Prove that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.