The sides of the trapezoid form corners of 60 with the lower base. The height of the trapezoid is 2 root of 3, and the middle line is 8. Find the lengths of the bases of the trapezoid?
Let’s draw the height BH of the trapezoid ABCD.
In a rectangular triangle ABH, the angle BAH = 60, then tg60 = BH / AH.
AH = BH / tg60 = 2 * √3 / √3 = 2 cm.
Since the angles at the base of the trapezoid are equal, the trapezoid is isosceles, which means that DP = AH = 2 cm.
Then BC = НР = АD – 4 cm.
According to the formula of the middle line of the trapezoid (BC + AD) / 2 = 8.
BC + AD = 16.
BC = AD – 4.
Let’s solve a system of two equations.
AD + AD – 4 = 16.
2 * AD = 20.
AD = 20/2 = 10 cm.
BC = 10 – 4 = 6 cm.
Answer: The lengths of the bases of the trapezoid are 10 cm and 6 cm.
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