Question

If the length of one base of a trapezoid is 5, the length of the other base is 2x + 7, and the length of the midsegment is 6x – 24, what is the value of x?

Answer 1

If the length of one base of a trapezoid is 5, the length of the other base is 2x + 7, and the length of the midsegment is 6x – 24,
whence 2(6x -- 24) = 5 + 2x + 7 Or x = 6


What is the length of the midsegment of the trapezoid made by the vertices A(0, 5), B(3, 3), C(5, -2) and D(-1, 2).
midsegment's length = sqrt[(--1/2 -- 4)^2 + (7/2 -- 1/2)^2] = (3/2) sqrt(13)


If the parallel sides of a trapezoid are contained by the lines y equals negative one-fourth x plus 5 and y equals negative one-fourth x minus 1,
the equation of the line that contains the midsegment is y = --(1/4) x + (5 -- 1)/2
Or y = --(1/4)x + 2