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Thread: Rectangle As A Function

  1. #1
    Senior Member harpazo's Avatar
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    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?
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    Re: Rectangle As A Function

    Quote Originally Posted by harpazo View Post
    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.

    Your answer would be correct if x was the width.
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    Senior Member harpazo's Avatar
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    Re: Rectangle As A Function

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

    Your answer would be correct if x was the width.
    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.
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    MHF Contributor MarkFL's Avatar
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    Re: Rectangle As A Function

    Quote Originally Posted by harpazo View Post
    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:

    $\displaystyle A(x)=\frac{1}{2}x^2$
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    Re: Rectangle As A Function

    Quote Originally Posted by harpazo View Post
    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).
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    Senior Member harpazo's Avatar
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    Re: Rectangle As A Function

    Quote Originally Posted by MarkFL View Post
    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.
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  7. #7
    Senior Member harpazo's Avatar
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    Re: Rectangle As A Function

    Quote Originally Posted by Debsta View Post
    "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.
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