Calculate the length of the height of an isosceles trapezoid if the lengths of its bases are 16 cm and 8 cm, and the length of the lateral side is √65 cm.
Let us lower the height BH and the height CK from the vertices of the obtuse angle.
Since, by condition, the trapezoid is isosceles, the segments cut off by the heights on the larger base are equal. AH = DK.
The BCKH quadrangle is rectangular, since BC is parallel to KH, and BH and CK are perpendiculars to AD, then HK = BC = 8 cm.
Then АH = DК = (АD – HК) / 2 = (16 – 8) / 2 = 8/2 = 4 cm.
From the right-angled triangle ABH, according to the Pythagorean theorem, we determine the length of the leg BH, which is the desired height of the trapezoid.
BH ^ 2 = AB ^ 2 – AH ^ 2 = (√65) ^ 2 – 4 ^ 2 = 65 – 16 = 49.
BH = 7 cm.
Answer: The height of the trapezoid is 7 cm.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.