 Hi and welcome to our session. Let us discuss the following question. The question says proof that the equilateral triangles described on two sides of a right-angled triangle are together equal to the equilateral triangle on the hypotenuse in terms of their areas. Now this is the right-angled triangle. We have to prove that equilateral triangles which are described on two sides of this triangle that is this triangle and this triangle is equal to the equilateral triangle which is described on the hypotenuse of this triangle that is this triangle in terms of its area. So let us now begin with the solution. Now let a b is equal to x units, c is equal to y units. Pythagoras theorem, a b square is equal to a b square plus b c square. Now a b is equal to x units and b c is equal to y units. Now this implies a c is equal to square root of x square plus y square. Now let us first recall the formula of area of an equilateral triangle. Area of an equilateral triangle is equal to root 3 by 4 into square of sight. Now let us first find area of triangle a b t. Now a b t is an equilateral triangle and each side is equal to x units. So area of triangle a b t is equal to root 3 by 4 into square of x. Now we will find area of triangle b e c is equal to root 3 by 4 into square of y. Now area of triangle a b t plus area of triangle b e c is equal to root 3 by 4 x square plus root 3 by 4 y square and this is equal to root 3 by 4 into x square plus y square. So area of triangle a b t plus area of triangle b e c is equal to root 3 by 4 into x square plus y square square units. Area of triangle a f c. Now each side of this triangle is equal to root of x square plus y square. So area of triangle a f c is equal to root 3 by 4 into square of root x square plus y square and this is equal to root 3 by 4 into x square plus y square squared units. So we have proved that area of triangle a b t plus area of triangle b e c is equal to area of triangle a f c. So this completes the session. Bye and take care.