In an isosceles trapezoid, the side is 10 cm, the larger base is 17 cm, and the height is 8 cm. Find the smaller base.
| February 17, 2021 | education
Let’s draw the heights of the ВK and CH trapezoid. The formed right-angled triangles AВK and СDН are equal in hypotenuse and acute angle, AB = СD since the trapezium is isosceles, and the angle ВAK = СDН. Then AK = DН, the length of which is determined by the Pythagorean theorem. AK ^ 2 = AB ^ 2 – ВK ^ 2 = 100 – 64 = 36.
AK = DK = 6 cm.
The length of the segment KН = AD – AK – DН = 17 – 6 – 6 = 5 cm.
The quadrilateral ВСНK is a rectangle, then ВС = KH = 5 cm.
Answer: The length of the smaller base is 5 cm.
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