In an isosceles trapezoid with a lateral side of 10 cm, a large base of 17 cm, a height of 8 cm. find a smaller base.
| May 16, 2021 | education
Draw two heights of the trapezoid from obtuse angles.
In a right-angled triangle ABH, we define, according to the Pythagorean theorem, the length of the leg AK.
AK ^ 2 = AB ^ 2 – ВK ^ 2 = 100 – 64 = 36.
AK = 6 cm.
Triangles ABK and CDH are equal, since the angle BAK = CDH, since these are the angles at the base of an isosceles trapezoid, AB = CD as lateral sides, then DH = AK = 6 cm.
Segment КН = АD – AK – DH = 17 – 6 – 6 = 5 cm.
Since BK and CH are heights, then BCHK is a rectangle, then BC = KH = 5 cm.
Answer: The smaller base is 5 cm.
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