The diagonals of a rectangular trapezoid are mutually perpendicular, and the large diagonal is divided

| April 26, 2021 | education

The diagonals of a rectangular trapezoid are mutually perpendicular, and the large diagonal is divided by the point of intersection into 2 cm and 8 cm segments.Find: the height

Since the diagonals of the trapezoid are perpendicular, then in the right-angled triangle ABD, the segment AO is the height drawn to the hypotenuse.

Then AO ^ 2 = OB * OD = 2 * 8 = 16.

AO = 4 cm.

In a right-angled triangle AOD, we determine the length of the hypotenuse AD. AD ^ 2 = AO ^ 2 + OD ^ 2 = 16 + 64 = 80.

Diagonal ВD = ОВ + ОD = 2 + 8 = 10 cm.

In a right-angled triangle ABD, according to the Pythagorean theorem, we determine the length of the leg AB.

AB ^ 2 = BD ^ 2 – AD ^ 2 = 100 – 80 = 20.

AB = √20 = 2 * √5 cm.

Since the trapezoid is rectangular, AB is its height.

Answer: The height of the trapezoid is 2 * √5 cm.



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