Question

For what value of X must ABCD be a parallelogram?

Answer 1

We know that:

• 
  `(AC)/(2) = 6x`

This means that:

• 
  `AC = (6x)(2) = 12x`
• 
  `AC = 12x = 6x + 7x - 9`

Step-by step calculations:

Simplify the RHS:

• 
  `12x = 6x + 7x - 9`
• =>
  `12x = 13x - 9`

Subtract 13x both sides:

• =>
  `-13x + 12x = 13x -13x - 9`
• =>
  `-x = -9`

Divide -1 both sides:

• =>
  `-x = -9`
• =>
  `(-x)/(-1) = (-9)/(-1)`
• =>
  `x = 9`

Answer 2

x = 9

Explanation:

If ABCD is a parallelogram, then 6x = 7x - 9

as the point of intersection of the 2 diagonals is the midpoint of AC

6x = 7x - 9

Subtract 6x from both sides:

⇒ 0 = x - 9

Add 9 to both sides:

⇒ 9 = x