# What are the sides of a right angled isosceles triangle?

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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.