Question

The side of a triangle ABC are in the ratio AB:BC :CA=1:ROOT2:1. SHOW that triangle ABC is a right angled triangle ,right angled at A.​

Answer 1

Answer:

AB:BC:AC = 1:√2:1

let AB be x

then, BC= √2 x

AC= x

BC²= (√2x)²

= 2x²

AB²+BC²= x²+ x²

= 2x²

since, AB² + CA² = BC²

by converse of phytagoras theorem

ABC is right angle triangle, right angled at angle A