since 2 of the right angled triangle are the same, we know we have an isosceles triangle. This means that the missing lengths are the same.
So we can do the following:
a² + b² = c²
x² + x² = 13²
2x² = 169 (collect the x values)
x² = 84.5 (divide both sides by 2)
x = √84.5
x = 9.2
So the length of one of the legs is 9.2