For a rectangular trapezoid, the sides are 9 cm and 15 cm and the smaller base is 14 cm, find the larger base.

Let ABCD be a rectangular trapezoid. Side AB = 9 cm, smaller base BC = 14 cm, side CD = 15 cm.
1. From point C draw the height CH to the larger base AD. Consider the triangle CHD. CHD is a right-angled triangle with a leg CH = 9 cm, since CH = AB (AB is in fact also a height and CH is parallel to AB), a hypotenuse CD = 15 cm and a second leg HD. Let us find the length of the leg HD according to the Pythagorean theorem:
HD = √ (CD ^ 2 – CH ^ 2);
HD = √ (15 ^ 2 – 9 ^ 2);
HD = √ (225 – 81);
HD = √144;
HD = 12 cm.
2. Since AB is parallel to CH and they form a right angle with the bases BC and AD, the quadrilateral ABCH is a rectangle. The width of the rectangle ABCH is sides AB and CH, and the lengths of the side are BC and AH. Since ABCH is a rectangle, BC and AH are equal.
Find the length of the larger base of the trapezoid ABCD:
AD = AH + HD;
AD = 14 + 12 = 26 (cm).
Answer: AD = 26 cm.