Parallelogram Perimeter: Finding the Expression When One Side is 4X

The longest sides of a parallelogram are X cm long and are four times longer than the shorter sides.

Express the perimeter of the parallelogram in terms of X.

Video Solution

Solution Steps

00:00 Express the perimeter of the parallelogram using X

00:03 Opposite sides are equal in a parallelogram

00:14 The larger sides in the parallelogram

00:23 The ratio of sides according to the given data

00:42 Let's mark side AB as X

00:56 We'll substitute the value of side AB to find AC

01:04 The perimeter of the parallelogram equals the sum of its sides

01:15 We'll substitute appropriate values and solve to find the perimeter

01:28 And this is the solution to the question

Step-by-Step Solution

In a parallelogram, each pair of opposite sides are equal and parallel: AB = CD and AC = BD.

Given that the length of one side is 4 times greater than the other side equal to X, we know that:

$AB=CD=4AC=4BD$

Now we replace the data in this equation with out own (assuming that AB = CD = X):

$x=x=4AC=4BD$

We divide by 4:

$\frac{x}{4}=\frac{x}{4}=AC=BD$

Now we calculate the perimeter of the parallelogram and express both AC and BD using X:

$P=x+\frac{x}{4}+x+\frac{x}{4}$

$P=2x+\frac{x}{4}+\frac{x}{4}=2\frac{1}{2}x$