The area of a trapezoid is:
(b1 + b2) * h/2, where b1 and b2 are the two bases and h is the height.
We are given expressions for the bases and values of the height and area, so let's plug the values in:
((x + 2) + (4x - 1)) * 8/2 = 104
Calculate the inside of the parentheses:
(5x + 1) * 8/2 = 104
8/2 = 4
(5x + 1) * 4 = 104
Divide by 4 on both sides:
5x + 1 = 26
Subtract 1 from both sides:
5x = 25
Divide by 5:
x = 5
Now that we know x, we can put it into the expressions given for the bases and figure out which is the longer one:
a = 4 * 5 - 1 = 20 - 1 = 19
b = 5 + 2 = 7
a is the longer base, so (A) is the answer.
