The base of the trapezoid is 2: 3 and the midline is 5 M. find the base of the trapezoid.

Given:

trapezoid ABCE,

АЕ and ВС – bases,

OH – middle line,

BC: AE = 2: 3,

OH = 5 meters.

Find the lengths of the bases of the trapezoid ABCE, that is, AE and BC -?

Solution:

Consider the trapezoid ABCE. The middle line is equal to the half-sum of the bases.

Let the length of the base BC = 2 * x meters, then the length of the base AE is equal to 3 * x meters. Composing the equation:

(2 * x + 3 * x): 2 = 5;

2 * x + 3 * x = 5 * 2;

2 * x + 3 * x = 10;

x * (2 + 3) = 10;

x * 5 = 10;

x = 10: 5;

x = 2 centimeters;

2 * 2 = 4 centimeters – the length of the base of the sun;

3 * 2 = 6 centimeters – AE base length.

Answer: 4 centimeters; 6 centimeters.