MN middle line of trapezoid ABCD. Find the bases of the trapezoid if BC: AD = 2: 3 and MN = 5cm.

Given:

trapezoid ABCD;

MN middle line;

BC: AD = 2: 3;

MN = 5 cm.

Find: BC, AD

Decision:

Let the BC base length be 2 * x centimeters, then the AD base length is 3 * x centimeters. We know that the middle line of a trapezoid is 5 centimeters. Let’s make the equation:

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

2x + 3x = 5 * 2;

2x + 3x = 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;

2 * 3 = 6 centimeters – the length of the AD base.

Answer: 4 centimeters; 6 centimeters.