A rectangular trapezoid is inscribed with a circle, the area of which is 130, the smaller side side 10. Find the larger side side.

1. The height h of a rectangular trapezoid ABCD, with right angles A and B, is equal to the smaller lateral side AB:

h = AB = 10.

2. The area of the trapezoid is equal to the product of the height and the half-sum of the bases:

S = h * (a + b) / 2 = h * (AD + BC) / 2, hence:

AD + BC = 2S / h = 2 * 130/10 = 26.

3. The sums of the opposite sides of the quadrangle in which the circle is inscribed are equal to each other:

AB + CD = AD + BC = 26,

from here we find the big side of the CD:

CD = AD + BC – AB = 26 – 10 = 16.

Answer: the large side of the trapezoid is 16.