Let abc be an isoscele right angle triangle, such that:
ab = bc
angle b = 90
Since ab = bc , then angle a = angle c
But angle a + angle c = 90
==> angle a = angle c = 45
We know that:
cosa = cos45
= sqrt2/2 = adjacent/hypotenuse
= sqrt2/2 = ab/ac
==> ab = bc = sqrt2.....(sides)
==> ac (hypotenuse) = 2
Since the right angled triangle is isoscles, we assume that its equal sides are the right angle making sides.
So applying the Pythagoras Theorem, the hypotenuse h should be.
h = sqrt (x^2+x^2) = sqrt(2x^2) = (sqrt2)x.
So any triangle with sides, (x , x and (2^(1/2)x for any value of x should represent a right angled triangle.
Also we can say if the ratio of the length of three sides of triangle are 1:1:2^(1/2) , then the triangle is a right angled triangle.