Question

Please help!! Picture is provided

Quad. ABCD is a trapezoid.
XY is the median
XY = 12; AB=16
Find DC

Answer 1

DC = 8

Explanation:

The median XY of the trapezoid ABCD is half or the sum of AB and DC.

XY = 1/2 ( AB + DC)

We need to find out DC so we can rewrite this equation isolating DC

XY = (1/2)(AB+DC), multiply both sides by 2

2XY = AB + DC, subtract from both sides AB

2XY - AB = DC, now substitute the given AB = 16 and XY = 12

2* 12 - 16 = DC , using the order of operations rules we multiply first

24 -16 = DC, subtract

8 = DC

Answer 2

DC = 8

Explanation:

The median is half the sum of the parallel bases, that is

`(AB+DC)/(2)` = XY , substitute values

`(16+DC)/(2)` = 12 ( multiply both sides by 2 to clear the fraction )

16 + DC = 24 ( subtract 16 from both sides )

DC = 8