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? Show equations and all work that leads to your answer.

Answer 1

The midsegment of a trapezoid is the arithmetic mean of the two parallel sides

http://www.9math.com/book/midsegment-trapezoid

so 6x-24 = (5 + 2x+7)/2
12x - 48 = 2x + 12
10x = 60
x = 6