In a rectangular trapezoid, the sides are 8 cm and 10 cm, and the larger base is 14 cm. Find the smaller base of the trapezoid.

Let ABCD be a rectangular trapezoid, BC – smaller base, AD = 14 cm – larger base, angle BAD – straight.
From the top of C we draw the height CH. CH cuts off the rectangle ABCH from the trapezoid ABCD (AB = CH = 8 cm, AH = BC = x cm) and the right triangle CHD: CD = 10 cm – hypotenuse, CH = 8 cm and HD – legs, angle CHD – straight line.
By the Pythagorean theorem, we find the length of the leg НD:
CD ^ 2 = CH ^ 2 + HD ^ 2;
100 = 64 + HD ^ 2;
НD ^ 2 = 36;
НD = √36 = 6 (cm).
Let’s find the length АН:
AD = AH + HD;
14 = AH + 6;
AH = 8 cm.
Since ABCH is a rectangle and AH = BC, then the smaller base BC = 8 cm.
Answer: BC = 8 cm.