One of the corners of a rectangular trapezoid is 120%, the large side is 20 cm and the middle line is 7 cm

| February 10, 2021 | education

One of the corners of a rectangular trapezoid is 120%, the large side is 20 cm and the middle line is 7 cm, find the base of the trapezoid.

Let’s denote the trapezoid ABCD, the angle С is equal to 120 °. From the top of corner C, we lower the height CH to the lower base AD. Consider a right-angled triangle CHD, in which the hypotenuse CD = 20 cm is known, the angle HCD = 120 ° – 90 ° = 30 °. The HD leg lies opposite an angle of 30 °, which means:
HD = 1/2 * CD = 10 (cm).
Let’s denote the smaller base BC x, then the base AD = (x + 10). By the condition, the middle line of the trapezoid is known, we get the equation:
(x + x + 10) / 2 = 7
2x + 10 = 14
2x = 4
x = 2 (cm) – smaller base of the BC.
x + 10 = 12 (cm) – larger base AD.
Answer: the bases of the trapezoid are 2 cm and 10 cm.



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