Question

a side of a triangle are in the ratio of 1 ratio root under 2 ratio 1 then prove that it is right triangle

Answer 1

ratio of sides are 1 : root 2 : 1

then let assume sides are AB = x , AC = x root 2 , BC = x

now we know that in a right angle triangle.

sum of square of 2 sides equal to square of 3rd side

AC = Root ( AB^2 + BC^2)

= root( x^2 + x^2)

= root( 2x^2)

= x root 2

hence it proves that these are sides of our right angle triangle