Question

Quadrilateral ABCD is a parallelogram with AB = 3y – 6, BC = 5x – 8, CD = 2y + 4, and AD = 4x –1. Find x.

A.
7
B.
14
C.
27
D.
28

Answer 1

In parallelogram ABCD, opposite sides are congruent, it means
AB = CD
BC = AD
So, 3y – 6 = 2y + 4 ........1
and 5x – 8 = 4x –1...........2
now we can find the value of x and y from expression 1 and 2,
3y – 6 = 2y + 4
3y-2y = 4+6
y = 10
5x – 8 = 4x –1
5x-4x = -1+8
x = 7
Thus, the value of x is 7, option A is the correct.