ABCD is a trapezoid, BF = 2.2. BC = 2.5. AD = 5. Find BD.

Let us prove that triangle BOS is similar to triangle AOD.

The BOC angle is equal to the AOD angle as the vertical angles at the intersection of the AC and BD diagonals.

The angle FBC is equal to the angle FDA as the cross-lying angles at the intersection of parallel straight lines BC and AD of the secant AD.

Then the triangles BOC and AOD are similar in two angles.

From the similarity of triangles: BC / BF = AD / DF.

DF = BF * AD / ВС = 2.2 * 5 / 2.5 = 4.4 cm.

Then BD = BF + DF = 2.2 + 4.4 = 6.6 cm.

Answer: The length of the diagonal BD is 6.6 cm.