Question

Quadrilateral ABCD is an isosceles trapezoid. If AB || CD , AB = m + 6, CD = 3m + 2, BC = 3m, and AD = 7m – 16, find BC. A8 B.9 C.10 D.12

Answer 1

I believe the answer is D from what I've calculated. 
Because ABCD is an isosceles trapezoid and AB is parallel to CD That means that BC and AD are equal to each other if you draw the picture with the facts given. But I got negative 12. Here's how:
 7m-16=3m   Set BC and AD equal in an equation. I could be wrong..
-7m       -7m   But I hope I helped. 
-16=-4m
+4    +4
m=-12

Answer 2

Answer: D.  12 unit

Step-by-step explanation:

Since, in an isosceles trapezoid, non parallel sides are always congruent or equal,

Here, in trapezoid ABCD,

AB = m + 6, CD = 3m + 2, BC = 3m, and AD = 7m – 16

Also, AB || CD ⇒ AB and CD are parallel,

⇒ BC and AD are non parallel sides,

Hence, by the above definition,

BC = AD

⇒ 3m = 7m - 16

⇒ -4m = -16

⇒ m = 4,

Hence, BC = 3m = 3×4 = 12 unit.

⇒ Option D is correct.