Find the bases of the trapezoid if its middle line is 16 cm and is divided by the diagonal into parts

Find the bases of the trapezoid if its middle line is 16 cm and is divided by the diagonal into parts, the difference of which is 6 cm

Given:

trapezoid ABCE,

OH – middle line,

OH = 16 centimeters,

AC – diagonal,

point E – the point of intersection of AC and OH,

ЕН – ОЕ = 6 centimeters.

Find bases AE and BC -?

Solution:

1. Consider the trapezoid ABCE. The middle line OH = OE + EH;

16 = OE + OE + 6;

16 = 2 * OE + 6;

16 – 6 = 2 * OE;

10 = 2 * OE;

OE = 10: 2;

OE = 5 centimeters;

EH = 5 + 6 = 11 (centimeters).

2. Consider the triangle ABC. The middle line OE = 1/2 * BC;

BC = 2 * OE;

BC = 2 * 5;

BC = 10 centimeters.

3. Consider the ACE triangle. Middle line ЕН = 1/2 * AE;

AE = 2 * EH;

AE = 2 * 11;

AE = 22 centimeters.

Answer: 10 centimeters; 22 centimeters.