Question

ABCD is a trapezoid with median EF. a. AB = 15, DC = 11, then EF = ? b. EF = 14, DC = 10, then AB = ? c. EF = 18, AB = (5n - 9), and DC = (2n + 3). Find n, AB, and DC. d. EF = (2y + 4), AB = (5y + 2), and DC = (-3y + 8). Find y, EF, AB, and DC.

Answer 1

The median of the trapezoid is the average of the bases. If we draw the trapezoid that is being described in this item, we will deduce that AB and DC are the bases and EF is given to be the median.

For this item,
EF = (AB + CD) / 2

Part A:
EF = (15 + 11) / 2 = 13

Part B:
AB = 2EF - CD
AB = (2)(14) - 10 = 18

Part C:
18 = ((5n - 9) + (2n + 3))/2
18 = (7n - 6) / 2
n = 6

Part D:
2y + 4 = ((5y + 2) + (-3y + 8))/2

y = 1

EF = 2(1) + 4 = 6
AB = (5(1) + 2 = 7
AB = -3(1) + 8 = 5