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

In a rectangular trapezoid, the sides are 9 cm and 15 cm, and the smaller base is 14 cm. Find the larger base of the trapezoid.

Let ABCD be a rectangular trapezoid. From the top of C to the larger base AD, draw the height CH. CH is parallel to AB, since AD and BC are perpendicular.
Consider a right-angled triangle CHD: leg CH = AB = 9 cm, hypotenuse CD = 15 cm.Let’s find leg HD:
HD = √ (CD ^ 2 – CH ^ 2) = √ (15 ^ 2 – 9 ^ 2) = √ (225 – 81) = √144 = 12 (cm).
AH = BC = 14 cm (since they are opposite sides of the ABCH rectangle).
AD = AH + HD;
AD = 14 + 12 = 26 (cm).
Answer: AD = 26 cm.