One of the bases of the trapezoid is 8cm larger than the other, and the middle line is 14cm. Find the base of the trapezoid.

The middle line of the trapezoid is equal to the half-sum of the bases: m = (a + b) / 2, where m is the middle line, a is the smaller base, b is the larger base. Let’s designate the smaller base as x, and the larger – x + 8. Then: (x + x + 8) / 2 = 14; (2x + 8) / 2 = 14; 2x + 8 = 28 (the basic rule of the “cross to cross” proportion); 2x = 28 – 8; 2x = 20; x = 20/2; x = 10 cm. Smaller base a = x = 10 cm. Larger base b = x + 8 = 10 + 8 = 18 (cm).
Answer: a = 10 cm, b = 18 cm.