Rectangle Perimeter: Solve for X When Area = 20 and Height = 4

Question

Look at the following rectangle:

The area of the rectangle is 20.

What is the perimeter of rectangle ABCD?

00:00 Calculate the perimeter of the rectangle

00:05 We'll use the formula for calculating rectangle area (side times side)

00:12 We'll substitute appropriate values according to the given data and solve for X

00:33 Open parentheses properly, multiply by each factor

00:48 Isolate X

01:02 This is the value of X, we'll substitute to find the side length

01:10 Opposite sides are equal in a rectangle

01:26 The perimeter of the rectangle equals the sum of its sides

01:32 We'll substitute appropriate values and solve for the perimeter

01:50 And this is the solution to the problem

The area of the rectangle equals length multiplied by width:

$S=AB\times AD$

Let's substitute the data into the formula:

$20=4\times(x+1)$

$20=4x+4$

$20-4=4x$

$16=4x$

$4=x$

Now we can calculate side AB:

$4+1=5$

The perimeter of the rectangle equals the sum of all sides together

Since in a rectangle each pair of opposite sides are equal, we can state that:

$AD=BC=4$

$AB=CD=5$

Now let's add all the sides together to find the perimeter:

$4+5+4+5=8+10=18$