Parallelogram Perimeter: Express Total Length When One Side is 2X

Question

A parallelogram has one side that is 2 times longer than the other. The length of the smaller side is X.

Express the circumference of the parallelogram in terms of X.

00:00 Express the perimeter of the parallelogram using X

00:03 Opposite sides are equal in a parallelogram

00:10 The larger pair of sides

00:16 The side length according to the given data

00:22 The ratio of sides according to the given data

00:29 Substitute the side value to find AB

00:34 Opposite sides are equal in a parallelogram

00:43 The perimeter of the parallelogram equals the sum of its sides

00:55 Substitute appropriate values and solve to find the perimeter

01:06 And this is the solution to the question

As is true of a parallelogram each pair of opposite sides are equal to one another

$AB=CD,AC=BD$

Given that $AB > AC$

Let's call AC by the name X and therefore:

$AB=2AC=2\times x=2x$

Now we know that:

$AB=CD=2x,AC=BD=x$

The perimeter is equal to the sum of all the sides together:

$2x+x+2x+x=6x$

4X+4