Question

Prove that the area of semi-circle dream on the hypothenuse of right angled triangle is equal to the sum of the equilateral triangle drawn on the other side of the triangle.​

Answer 1

Step-by-step explanation:

Let RST be a right triangle at S and RS = y, ST = x. Three semi-circles are draw on the sides RS, ST and RT, respectively A1, A2 and A3. To prove A3 = A1 + A2 In ∆RST, by Pythagoras theorem, RT2 = RS2 + ST2 = RT2 = y2 + x2 ∴ Area of semi-circle drawn