Question

If the sides of a triangle are in the ratio 1:root2 :1 show that it is aright angled triangle

Answer 1

Let the side length be x ,x√2 and x

If it is right angled triangle, it will follow Pythagoras Theorem.
hypothenuse²  = base² + height²
⇒(x√2)² = (x)² +(x)²
⇒2x² = 2x²

This means this is a right angled triangle.

Answer 2

let,
the sides of the triangle be,
x , √2x and x
in a right angled triangle,
(HYP)² = sum of squares of  other two sided
(√2x)² = x²+x²
⇒ 2x² = 2x²
therefore,
If the sides of a triangle are in the ratio 1:root2 :1, it is a right angled triangle