In a rectangular trapezoid, the diagonals are perpendicular, the height is 2. find the top base if the bottom is 3.

Let us prove the similarity of triangles ABC and BAD.

Let the angle BAC = X0, then the angle CAD = (90 – X) 0.

Since the diagonals are perpendicular, the triangle AOD is rectangular, then the angle BAD = 180 – 90 – (90 – X) = X0.

Angle BAC = BAD, then triangles ABC and BAD are similar in acute angle.

Then BA / AD = BC / BA.

BA ^ 2 = AD * BC.

BC = BA ^ 2 / AB = 4/3 = 1 (1/3) cm.

Answer: The length of the smaller base is 1 (1/3) cm