Good Morning, Shelley,
The formula or equation to determine the area - which is what you want to do with this problem - is A = L * W where A equals area, L equals length, * is the sign for multiplying, and W is width.
You do not know what the width of this rectangle is, right? But you do know what the length is.
Therefore, let's assign the value of x to the width, and the value of 2x to the length, fair enough?
Please note from the problem:
"The length of a rectangle is twice that of its width."
Now, we can plug in these values and solve the equation for x.
A = L * W
72 = x * 2x
72 = 2x2
Divide both sides of your equation by two leaving x2 to itself, okay.
36 = x2
To get rid of the radical all you need do is take the square root of each side and when you do this, you are left with x, right?
x = 6
Remember our equation from earlier and the information from the problem: "The length of a rectangle is twice that of its width?" We just solved for the width. Do you see that?
Now, we also know that the length is twice the width meaning it is 2 (x) or 12. Therefore, your dimensions are:
W = 6
L = 12
Let's check our work, shall we?
The best way I recommend is to determine whether your answer proofs is to use the same equation. In this case it is the equation for Area. A = L * W
Is the following true when we plug in our values?
72 = 6 *12
72 = 72 Yes it checks. Is the length twice that of its width in the rectangle. Yes.
I hope I have assisted you and wish you a good day. Please feel free to leave any feedback underneath this answer in the comment section below. If you need additional assistance, feel free to reach out to any tutor.