The middle line of a rectangular trapezoid is 14 cm, and its height, drawn from the top of an obtuse angle

| September 1, 2021 | education

The middle line of a rectangular trapezoid is 14 cm, and its height, drawn from the top of an obtuse angle, divides the base in a ratio of 3: 1, counting from the top of the right angle. Find the basics of the trapezoid.

Let the segment DH, the base AD be equal to X cm, then, by condition, the length of the segment AH will be equal to 3 * X cm.

Base length AD = AH + DH = 3 * X + 4 * X = 7 * X.

Quadrangle ABCН is a rectangle, since the segments AB and CH are perpendicular to the bases BC and AD. Then the length of the base BC = AH = 3 * X cm.

According to the formula of the middle line of the trapezoid: KM = (BC + AD) / 2.

14 = (3 * X + 4 * X) / 2.

7 * X = 28.

X = 28/7 = 4.

Then BC = 3 * 4 = 12 cm.

AD = 4 * 4 = 16 cm.

Answer: The bases of the trapezoid are 12 cm and 16 cm.



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