In an isosceles trapezoid, the lengths of the segments by which the height drawn

| May 24, 2021 | education

In an isosceles trapezoid, the lengths of the segments by which the height drawn from the top of the obtuse angle divides the larger base is 1: 2, then the ratio of the lengths of the bases is?

Let’s draw two heights of the trapezoid ВK and CH.

Let the length of the segment DH = X cm, then, by condition, the length of the segment AH = 2 * X cm.

In right-angled triangles ABK and CDH, side AB = CD as lateral sides of an isosceles trapezoid, angle BAK = CDH as angles at the base of an isosceles trapezoid. Then the triangle ABK and CDH are equal in hypotenuse and acute angle, which means AK = DH = X cm.Then KH = AH – AK = 2 * X – X = X cm.

Quadrangle ВСНK is a rectangle, then BC = KH = X cm.

AD = AH + DH = 2 * X + X = 3 * X.

BC / AD = X / 3 * X = 1/3.

Answer: The bases of the trapezoid are referred to as 1/3.



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