EF is a median of trapezoid ABCD. If the length of EF is 14x, and the length of CD is 20x, what is the length of AB in terms of x?
Which sides are parallel ?
To find the length of AB in terms of x, we need to establish a relationship between the sides of the trapezoid.
A trapezoid is defined as a quadrilateral with one pair of parallel sides. In this case, AB and CD are the parallel sides.
Since EF is stated as a median, it means that it divides the trapezoid into two equal areas. Therefore, the lengths of the segments EC and FD are equal.
Let's assume the length of EC and FD is y. Then, we can find the lengths of AD and BC using the given lengths of CD and EF:
AD = CD - 2 * EC
BC = CD - 2 * FD
Since EC = FD = y, we set up the equations:
AD = 20x - 2y
BC = 20x - 2y
Next, we want to find the length of AB. Since AB and CD are parallel sides, they have the same length. Hence, AB = CD = 20x.
Therefore, the length of AB in terms of x is 20x.