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

Given:
ABCE trapezoid,
ВС and АЕ – bases,
AE = BC + 8 centimeters,
KO is the middle line of the trapezoid,
KO = 14 centimeters.
Find the lengths of the bases, that is, BC and AE -?
Decision:
Consider the trapezoid ABCE.
Let the lengths of the base BC = x centimeters, then the length of the base AE = x + 8 centimeters. We know that the middle line is equal to the half-sum of its bases. We compose the equations:
(x + x + 8) * 1/2 = 14;
x + x + 8 = 2 * 14;
x + x + 8 = 28;
x + x = 28 – 8;
x + x = 20;
x * (1 + 1) = 20;
x * 2 = 20: 2;
x = 10 centimeters – the length of the base of the sun;
10 + 8 = 18 centimeters – AE base length.
Answer: 10 centimeters; 18 centimeters.