An isosceles triangle has two long side and one short side , the short side is half the length of a long side, find the short side,

Let the length of the short side be x, and the length of the long side be 2x (since the short side is half the length of a long side).

The two long sides of the triangle are equal, so:

2x = 2x

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So:

2x + 2x > x

4x > x

3x > 0

Therefore, x must be greater than 0.

Now we can solve for x:

2x = 2x

2x + 2x > x

4x > x

3x > 0

x > 0

x = 2x/2

x = 2x รท 2

x = x

Therefore, the length of the short side is x, which is half the length of the long side.