Prove that the area of the semicircle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the semicircles drawn on the other two sides of the triangle

Prove that the area of the equilateral triangle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the equilateral triangles drawn on the other two sides of the triangle.

Prove that the area of the equilateral triangle drawn on the hypotenuse of a right angle triangle is equal to the sum of the areas of the equilateral triangles drawn on the other two sides.

If the area of the square drawn on any side of a triangle is equal to the sum of the areas of the squares drawn on the other two sides of the triangle ,then the triangle will be right-angled triangle, the opposite angle of the greatest side of which will be "......................" .

A perpendicular AD is drawn on BC from the vertex A of the acute Delta ABC . Prove that AC^(2) = AB^(2) +BC^(2) -2BC.BD OR Prove that the square drawn on the opposite side of theacute angle of an acute triangle is equal to the areas of the sum of the squares drawn on its other two sides being subtracted by twice the area of the rectangle formed by one of its sides and the projection of the other side to this side.

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.

Prove that the sum of the areas of the squares drawn on the sides of a rhombus is equal to the sum of the areas of two squares drawn on the diagonals of the given square.

In a right-angled triangle, the area of a square drawn on the hypotenuse is equal to the "…..............." of the areas of the squares drawn on other two sides.

Answer any one : If in a triangle, the area of the square drawn on one side is equal to the sum of the areas of the squares drawn on other two sides, then prove that the angle opposite to the first side will be a right angle.

Prove that "In a right angled triangle the square of hypotenuse is equal to the sum of the square of the other two sides".