Question

If the sides of the triangle are in the ratio 1: `sqrt2`: 1, show that is a right-angled triangle.

Answer 1

Let, the sides of the triangle be, x: `sqrt2`x and x.

AB² + BC² = x² +x² = 2x²

AC² = `(sqrt2 x)^2` = 2x²

AB² + BC² = AC² 

Conversely, if in any triangle, the square on the largest side of the triangle is equal to the sum of the squares on remaining two sides, then the triangle is a right-angled triangle and the angle opposite to the largest side is a right-angle.

Therefore, Δ ABC is a right-angled triangle.