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

August 30, 2021 | education

| 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.

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