The base of the trapezoid is 2: 3 Its middle line is 24 inches. Find the base of the trapezoid.

Given:
trapezoid ABCE,
EO – middle line,
АЕ and ВС – bases,
AE: BC = 3: 2,
EO = 24 decimetres.
Find the bases of the trapezoid, that is, AE and BC -?
Solution:
Consider the trapezoid ABCE. Let the length of the base BC = 2 * x centimeters, then the length of the base AE = 3 * x centimeters. We know that the length of the midline is 24 decimetres = 240 centimeters. Let’s make the equation:
(2 * x + 3 * x): 2 = 240;
x * (2 + 3) = 480;
x * 5 = 480;
x = 480: 5;
x = 96 centimeters;
96 * 2 = 192 centimeters – the length of the base of the sun;
96 * 3 = 288 centimeters – the length of the base AE.
Answer: 192 centimeters; 288 centimeters.