# Thread: Rectangle As A Function

1. ## Rectangle As A Function

Express the area A of a rectangle as a function of the length x if the length is twice its width.

Width = x

Length = 2x

So, A(x) = (2x)(x), which leads to 2x^2 as my final answer.

The book's answer is A(x) = (1/2)x^2.

I say the book is wrong. What do you say?

2. ## Re: Rectangle As A Function

Originally Posted by harpazo
Express the area A of a rectangle as a function of the length x if the length is twice its width.

Width = x

Length = 2x

So, A(x) = (2x)(x), which leads to 2x^2 as my final answer.

The book's answer is A(x) = (1/2)x^2.

I say the book is wrong. What do you say?
Read the question more carefully. It says that Length = x. So therefore Width = 1/2 *x and so their answer is correct.

3. ## Re: Rectangle As A Function

Originally Posted by Debsta
Read the question more carefully. It says that Length = x. So therefore Width = 1/2 *x and so their answer is correct.

But it says the length is TWICE its width. I understand this to mean that the width is x and length 2x (twice its width). Sorry but I don't get it.

4. ## Re: Rectangle As A Function

Originally Posted by harpazo
But it says the length is TWICE its width. I understand this to mean that the width is x and length 2x (twice its width). Sorry but I don't get it.
Length is twice the width:

$\displaystyle \ell=2w\implies w=\frac{1}{2}\ell$

$\displaystyle A=\ell w=\frac{1}{2}\ell^2$

And so if:

$\displaystyle \ell=x$

We have:

$\displaystyle A(x)=\frac{1}{2}x^2$

5. ## Re: Rectangle As A Function

Originally Posted by harpazo
But it says the length is TWICE its width. I understand this to mean that the width is x and length 2x (twice its width). Sorry but I don't get it.
"The length is TWICE its width" is the same as saying "The width is HALF its length". And the question specifies that x is the LENGTH (not the width).

6. ## Re: Rectangle As A Function

Originally Posted by MarkFL
Length is twice the width:

$\displaystyle \ell=2w\implies w=\frac{1}{2}\ell$

$\displaystyle A=\ell w=\frac{1}{2}\ell^2$

And so if:

$\displaystyle \ell=x$

We have:

$\displaystyle A(x)=\frac{1}{2}x^2$
Ok. So I'm wrong again.

7. ## Re: Rectangle As A Function

Originally Posted by Debsta
"The length is TWICE its width" is the same as saying "The width is HALF its length". And the question specifies that x is the LENGTH (not the width).
I will post a few more like this one when time allows.