Express the area A of a rectangle as a function of the width W if the length of the rectangle is twice its width.
Area A of a rectangle is ____
The wording has me really confused all I know is A= L*W
I
L = 2W
A = L*W = 2W*W = 2W^2
makes sense, since the area of a square with side W is W^2, and you basically have two squares, right?
Ah, don't worry, my friend! I'm here to help you unravel the mystery of this rectangle's area! Let's dive into it with a splash of humor, shall we?
Now, you're absolutely right that the formula for the area of a rectangle is A = L * W. But fear not, for we can still work it out even if we don't know the exact value for L just yet.
Here's what we do know: the length (L) of the rectangle is twice its width (W). So instead of sticking with L, let's substitute it with 2W in the formula.
Voila! We now have A = 2W * W. But since 2W is basically just double the width, we can simplify it further.
So the final expression for the area A of the rectangle, my whimsical friend, comes down to A = 2W^2. Ta-da!
Now you have a quadratic function describing the area of the rectangle in terms of its width. Isn't math funny? It's like juggling numbers and concepts in a circus act!
No worries! I can help clear up the confusion.
In this case, the length (L) of the rectangle is given as twice the width (W). So we can express the length as L = 2W.
Now, let's recall the formula for the area (A) of a rectangle: A = L * W.
Substituting the value of L, our formula becomes A = (2W) * W.
Simplifying this, we have A = 2W^2.
Therefore, the area (A) of the rectangle can be expressed as a function of the width (W) as A = 2W^2.
To express the area A of a rectangle as a function of the width W, we need to use the given information that the length of the rectangle is twice its width.
Let's start with the formula for the area of a rectangle, which is A = L * W, where L is the length and W is the width.
Since the length of the rectangle is twice its width, we can write L = 2W.
Now we can substitute this value of L into the formula for the area:
A = (2W) * W
Simplifying this expression, we get:
A = 2W^2
So, the area A of the rectangle can be expressed as the function A(W) = 2W^2, where W is the width of the rectangle.