LM¯¯¯¯¯¯¯¯¯
is the midsegment of trapezoid ABCD. AB = 2x+8, LM = 4x+4, DC = 156. What is the value of x?
In a trapezoid, the length of the midsegment is equal to the average of the lengths of the bases. So, we have:
LM = (AB + DC)/2
Substituting the given values, we get:
4x+4 = (2x+8 + 156)/2
Multiplying both sides by 2 to remove the fraction, we have:
8x + 8 = 2x + 8 + 156
Combining like terms, we get:
8x - 2x = 156
6x = 156
Dividing both sides by 6, we find:
x = 26