As shown in the figure, in △ ABC, ad bisects ∠ BAC, de ‖ AC, EF ‖ BC, ab = 15, AF = 4, then de=______ .

As shown in the figure, in △ ABC, ad bisects ∠ BAC, de ‖ AC, EF ‖ BC, ab = 15, AF = 4, then de=______ .

Let ed = x, then AC = 4 + X. ∵ ad bisector ∠ BAC. From the bisector theorem of triangle inner angle, we get ABAC = bddc = 154 + X and deca = bdbc. ∵ XX + 4 = 1519 + X, and the solution is x = 6 (x = - 10, rounding off), so the answer is 6