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 Calculate X

00:03 Use the formula for calculating rectangle area (length times width)

00:13 Substitute appropriate values according to the given data and solve for X

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

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

01:14 Take half X out of the parentheses

01:26 Find the solution options for X

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

01:40 And this is the solution to the problem

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.

$x=36$