Question

i) In a right angled triangle, equilateral triangles are drawn on its all sides. Show that the sum of the areas of triangles on perpendicular sides is equal to the area of triangle on hypotenuse​

Answer 1

Step-by-step explanation:

We know that in a right angled triangle by Pythagoras theorem

a²+b²=c² ......................(i)

Also sides of the equilateral triangles will be a, b, c

Therefore areas of the equilateral triangle wil be √3a²/4,√3b²/4, √3c²/4

Now multiplying (i) by √3/4 we get

√3a²/4+√3b²/4=√3c²/4

This simply means that the sum of the areas of triangles on perpendicular sides is equal to the area of triangle on hypotenuse​