Calculate X: Rectangle Area = 22x with Side Length (x+8)

Question

The area of the rectangle below is equal to 22 $x$ .

Calculate $x$ .

00:00 Determine the value of X

00:03 Apply the formula for calculating the area of a rectangle (length x width)

00:13 Substitute in the relevant values according to the given data and proceed to solve for X

00:32 Open the parentheses and multiply 0.5X by the 2 factors

00:57 Arrange the equation so that we have 0 on one side

01:14 Take half X out of the parentheses

01:26 Determine the solution options for X

01:37 X must be greater than 0 given that it's a length of a side

01:40 This is the solution

The area of a rectangle is equal to its length multiplied by its width.

Let's write out the known data:

$22x=\frac{1}{2}x\times(x+8)$

$22x=\frac{1}{2}x^2+\frac{1}{2}x8$

$22x=\frac{1}{2}x^2+4x$

$0=\frac{1}{2}x^2+4x-22x$

$0=\frac{1}{2}x^2-18x$

$0=\frac{1}{2}x(x-36)$

For the equation to be balanced, $x$ needs to be equal to 36.

$x=36$