LM¯¯¯¯¯¯¯¯¯
is the midsegment of trapezoid ABCD. AB = 2x+8, LM = 4x+4, DC = 156. What is the value of x?
(2 points)
Since LM is the midsegment of trapezoid ABCD, LM is parallel to both AB and DC and its length is equal to the average of the lengths of AB and DC.
Therefore, we can set up the following equation:
LM = (AB + DC)/2
Substituting the given values, we have:
4x + 4 = (2x + 8 + 156)/2
Simplifying the right side, we have:
4x + 4 = (2x + 164)/2
Multiplying both sides by 2, we have:
8x + 8 = 2x + 164
Subtracting 2x from both sides, we have:
6x + 8 = 164
Subtracting 8 from both sides, we have:
6x = 156
Dividing both sides by 6, we have:
x = 156/6
Simplifying, we have:
x = 26
Therefore, the value of x is 26.