Rectangle Side Length: Solve for X When Area = 64 cm² and AB = 4BC

Question

Given the rectangle ABCD

BC=X and the side AB is 4 times greater than the side BC:

The area of the rectangle is 64 cm².

Calculate the size of the side BC

00:14 Let's find the length of side B C.

00:18 Remember, to calculate the area of a rectangle, multiply side A B by side B C.

00:38 Now, let's plug in the values we know into this equation.

00:45 We're told that side A B is four times longer than side B C.

00:59 So, let's put this into our formula and figure out what X is.

01:27 And that's how we solve this problem!

The area of the rectangle equals:

$S=AB\times BC$

$64=AB\times X$

Since it is given that side AB is 4 times larger than side BC

We can state that:

$AB=4BC=4X$

Now let's substitute this information into the formula for calculating the area:

$64=4x\times x$

$64=4x^2$

Let's divide both sides by 4:

$16=x^2$

We'll take the square root as follows:

$4=x$

In other words, BC equals 4