LM is the midsegment of trapezoid ABCD. AB = 2x+8, LM = 4x+4, DC = 156. What is the value of x?
Since LM is the midsegment of trapezoid ABCD, we know that LM is parallel to AB and that its length is equal to the average of the lengths of the bases.
In this case, the length of AB is 2x+8 and the length of DC is 156. Therefore, the average of the lengths of the bases is (2x+8+156)/2 = (2x+164)/2 = x+82.
But we also know that LM has length 4x+4. So we can set up the equation 4x+4 = x+82 and solve for x:
4x+4 = x+82
3x = 78
x = 78/3
x = <<26=26>>26
Therefore, the value of x is 26.