Given a rectangular trapezoid, its middle line is 9, the larger side side is 24, 1 of the corners adjacent to the side side is 2 times larger than the other. Find the base of a trapezoid
Determine the angles of the trapezoid at the lateral side of the CD. Let the angle СDА = X0, then, by condition, the angle ВСD = 2 * X0. The sum of the angles of the trapezoid pi of the lateral base is 180, then (X + 2 * X) = 180.
3 * X = 180.
X = 180/3 = 60.
Let’s draw the height of the trapezoid CH, then in the right-angled triangle SDN the angle DСН = 180 – 90 – 60 = 30. Then the leg DН lies opposite the angle 30, which means DН = СD / 2 = 24/2 = 12 cm.
Let the length BC = X cm, then AH = X cm.
According to the formula of the middle line of a trapezoid. KM = (BC + AD) / 2 = (X + X + 12) / 2 = 9.
2 * X = 18 – 12 = 6.
X = BC = AH = 6/2 = 3 cm.Then AD = 3 + 12 = 15 cm.
Answer: The bases of the trapezoid are 3 cm and 15 cm.
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