The diagonal of a rectangular trapezoid and its side are equal to find the length

The diagonal of a rectangular trapezoid and its side are equal to find the length of the midline if the height of the trapezoid is 2 cm and the side is 4 cm.

Given:

rectangular trapezoid ABCE,

AB = 2 centimeters,

AC = CE = 4 centimeters,

OH is the middle line.

Find the length of the midline OH -?

Decision:

1. Consider a right-angled triangle ABC.

Then, by the Pythagorean theorem (the square of the hypotenuse is equal to the sum of the squares of the legs):

AB ^ 2 + BC ^ 2 = AC ^ 2:

2 ^ 2 + BC ^ 2 = 4 ^ 2;

4 + BC ^ 2 = 16;

BC ^ 2 = 16 – 4;

BC ^ 2 = 12;

BC = 2√3 centimeters.

2. Consider the ACE triangle. It is isosceles since AC = CE. Let’s draw the height of the SC. She is the median. Then AK = KE = 2√3 centimeters. Therefore, the base AE = 4√3.

3. OH = (BC + AE): 2 = (4√ 3 + 2√ 3): 2 = 3√ 3 centimeters.

Answer: 3√ 3 centimeters.