the perimeter of a triangle P = a + b + c, where a, b and c are the lengths of the sides of the triangle

we also know that the legs are equal that is a = b = x

using the Pythagorean Theorem for c we have

c^2 = a^2 + b^2

c^2 = x^2 + x^2

c^2 = 2 (x^2)

c = (2(x^2))^0.5

c = x*(2^0.5)

finally for the perimeter we have

P = x + x + x*(2^0.5)

P = 2x + x*(2^0.5)

P = x(2 + (2^0.5))

the relationship between the leg x and the perimeter P is given by the equation P = x(2 + (2^0.5)).