In a parallelogram ABCD, AB=x+4, BC=3x, and CD=4x-4. ABCD must be a?

Question

i am confused about this question. 

these are the choices:

A: rectangle 

B: rhombus

C: trapezoid

D:Square

E: pentagon

 

Answer 1

Well, let's lule out pentagon (E), for sure!

 

If this is a rhombus, (which includes square) then x+4 = 3x  and also 3x = 4x + 4.

 

The latter implies x = -4.  NO GOOD! this rules out D and B.

 

If a rectangle, then x+4 = 4x-4, meaning that 3x = 8 (AB = CD).  This is possible.

 

The parallelogram ABCD can be a rectangle. It cannot be a trapezoid because its opposite pairs of sides are not both equal.