The bases of an isosceles trapezoid are 50 and 104, the lateral side is 45. Find the length of the diagonal of the trapezoid.

You are given an isosceles trapezoid ABCD, where BC and AD are the bases, AB and CD are the sides.
BC = 50 cm, AD = 104 cm.
MN = BC = 50.
AM + ND = 104-50 = 54.
AM = ND = 54/2 = 27 cm.
Let’s find the height of the VM as the leg of the triangle ABM:
BM ^ 2 = AB ^ 2-AM ^ 2 = 45 ^ 2-27 ^ 2 = 2025-729 = 1296.
BM = 36.
Next, we find the diagonal of the trapezoid BD as the hypotenuse of the triangle MBD.
MD = 50 + 27 = 77.
BD ^ 2 = BM ^ 2 + MD ^ 2 = 36 ^ 2 + 77 ^ 2 = 1296 + 5929 = 7225.
BD = 85 /
Answer: 85.