Parallelogram Perimeter Problem: Find X When AB = 6 and Perimeter = 20

Question

Look at the parallelogram shown below.

AB = 6

AC = X

The perimeter of the parallelogram is 20.

Find X.

00:00 Find X

00:03 Opposite sides are equal in a parallelogram

00:12 They are also a pair of opposite sides, therefore equal

00:24 The perimeter of the parallelogram equals the sum of its sides

00:38 Let's substitute appropriate values and solve for X

00:54 Isolate X

01:02 And this is the solution to the question

As is true for a parallelogram each pair of opposite sides are equal:

$AB=CD=6,AC=BD=x$

Calculate X according to the given perimeter:

$20=6+6+x+x$

$20=12+2x$

$20-12=2x$

$8=2x$

$x=4$