Question

prove that the equilateral triangle described on the two sides of a right angle triangle are together equal to the equilateral triangle on the hypotenuse in terms of their areas

Answer 1

let sides of right angled triangle be a,a, and √2a.
area of equilateral triangle from first side is 1÷2×base ×height
hence area=1÷2×a×√3a/2
=√3/4asquare
area of triangle of another triangle is also equal to first one .so sum of area of 2triangles is 2×√3/4asquare which is equal to √3/2asquare
now area of triangle from hypotenuse is
1÷2×base×height
1÷2×√2a×√3/√2a
answer will be √3/2asquare which is equal to sum of areas of triangles from other two sides .please make diagram yourself.

Answer 2

Answer:

the answer is attached