Question

determine whether the triangle having sides(2a-1)cm,2 root2a cm and (2a+1)cm is a right angled triangle

Answer 1

We have to determine whether the triangle having sides (2a - 1) cm, 2√2a cm and (2a + 1) cm is a right angled triangle.

Solution : Let ABC is a triangle where AB = (2a - 1)cm , BC = 2√2a cm and CA = (2a + 1) cm

from Pythagoras theorem,

if ∆ABC is right angled at B,

then CA² = AB² + BC²

if ∆ABC is right angled at C,

then AB² = BC² + CA²

if ∆ABC is right angled at A,

then BC² = CA² + AB²

let CA = (2a + 1) is the largest side of ∆ABC

then, CA² = (2a + 1)² = 4a² + 4a + 1

and AB² + BC² = (2a - 1)² + (2√2a)²

= 4a² - 4a + 1 + 8a = 4a² + 4a + 1

here it is clear that CA² = AB² + BC²

therefore ABC is right angled at B. means, (2a + 1) is hypotenuse.