Let h = height of triangle (from vertex to side x)

Draw that height line: you'll end up with 2 right triangles sides 8, x/2 and h ; ok?

So (pythagorean theorem): h^2 + x^2/4 = 64 [1]

Area = height * base / 2

So hx/2 = 24 ; hx = 48 ; h = 48/x [2]

Substitute [2] in [1]:

(48/x)^2 + x^2/4 = 64

Solve for x