Parallelogram Perimeter Problem: Solving for X when Perimeter is 80 cm

Question

The parallelogram ABCD has a perimeter equal to 80 cm.

Calculate X.

00:00 Find X

00:04 The perimeter of a parallelogram equals the sum of its sides

00:07 Opposite sides are equal in a parallelogram, so multiply each side

00:12 Substitute appropriate values according to the given data, and solve for X

00:20 Collect like terms

00:24 Isolate X

00:31 And this is the solution to the problem

Since in a parallelogram each pair of opposite sides are equal and parallel:

$BC=AD=2x$

$AB=CD=x$

Now let's substitute the known data into the formula for calculating the perimeter:

$80=2x\times2+2\times x$

$80=4x+2x$

$80=6x$

Let's divide both terms by 6:

$\frac{80}{6}=\frac{6x}{6}$

$\frac{80}{6}=x$

Let's simplify the fraction by 2

$\frac{40}{3}=x$

$x=\frac{40}{3}$