If the sides of a triangle are in the ratio 1:√2:1, show that it is a right-angled triangle.
As we observe that the greatest side of the given triangle is √2.
In given right angled triangle, say a=x,b=√2x,c=x then
Using Pythagoras theorem,
a2+c2=b2
LHS=a2+c2=x2+x2=2x2 unit,
RHS=b2=(√2x)2=2x2 unit,
LHS=RHS
Hence, If the sides of a triangle are in the ratio 1:√2:1, then it is a right-angled triangle.