Parallelograms

Question

In parallelogram ABCD, AB=4x-3 and CD=2x+5. Find the length of AB. If AD=5z-7, what kind of quadrilateral could ABCD be? Why?

Answer 1

A parallelogram has 2 sides that are equal in length and another 2 sides of equal length. Therefore, we can set side AB equal to side CD and solve for x.  4x-3=2x+5

x=4

We then substitute the value of x back into the equation for side AB and get the length.

4*4-3=13

The length of side AB is 13.

 

The parallelogram could be a rhombus or a square.  There is nothing stating that all four sides were not equal.  If the sides were equal, then the value of z would be 4.

5z -7=13

z=4