Calculate Rectangle Side Length: Given Area 24 cm² and Partial Measurements

Shown below is the rectangle ABCD.

Given in cm:

AK = 5

DK = 4

The area of the rectangle is 24 cm².

Calculate the side AB.

Let's look at triangle ADK in order to calculate side AD:

$AD^2+DK^2=AK^2$

Now let's substitute in our values:

$AD^2+4^2=5^2$

$AD^2+16=25$

We'll then move 16 to the other side and change the sign to the appropriate one:

$AD^2=25-16$

$AD^2=9$

Next, we'll take the square root and get:

$AD=3$

Since AD is a side of rectangle ABCD, we can calculate side AB as follows:

$S=AB\times AD$

Let's substitute in our values:

$24=3\times AB$

Finally, we'll divide both sides by 3:

$AB=8$