The sides of the trapezoid form corners of 60 with the lower base.
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.