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Math Help - word problem dont know were to start

  1. #1
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    word problem dont know were to start

    Hi, I am really stuck on this question ,

    fig.19.2 shows a template whose area is 50 square centimetres. find the total length of the template.

    I have drawn the image on paint and have attached it, but its not a very good drawing. sorry if it does not make much sense to you!

    I would be able to work this out if it was just the square but because there’s also this semi-circle shape attached to the square i don't really know how to calculate the length of it.
    Attached Thumbnails Attached Thumbnails word problem dont know were to start-untitled.jpg  
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  2. #2
    Senior Member Peritus's Avatar
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    <br />
\begin{gathered}<br />
Area_{template}  = x^2  + \frac{{\pi \left( {\frac{x}<br />
{2}} \right)^2 }}<br />
{2} = 50 \\<br />
  Length_{template}  = 3x + \frac{{\pi x}}<br />
{2} \hfill \\ <br />
\end{gathered} <br />

    good luck...
    Last edited by Peritus; October 17th 2008 at 06:57 AM.
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  3. #3
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    Quote Originally Posted by Peritus View Post
    <br />
\begin{gathered}<br />
  Area_{template}  = x^2  + \pi \left( {\frac{x}<br />
{2}} \right)^2  = 50 \hfill \\<br />
  Length_{template}  = 3x + \frac{{\pi x}}<br />
{2} \hfill \\ <br />
\end{gathered} <br />

    good luck...
    I don't really understand how you got to your final 2 equations could you please explain it step my step? please

    thanks!

    p.s. what do I do with the length of the square? which is 6cm? where am I suppose to use that?
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  4. #4
    Senior Member Peritus's Avatar
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    let us denote the side of the square by x.
    The area of the square is x^2.
    From your drawing I understand that there's a half circle on the rightmost side of the square, so basically the diameter of the circle equals the side of the square (x). We know that the area of a circle is:
    <br />
\pi r^2

    where r is the radius of the circle (the diameter is twice the radius).
    So we can express the area of the half circle using x, like so:

    <br />
\frac{{\pi \left( {\frac{x}<br />
{2}} \right)^2 }}<br />
{2}

    the area of the template is the sum of the square area and the half circle area, and that's how we get the first equation, I hope that you can figure out the second equation now.
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  5. #5
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    I kind of understand the first equation, but i am still not sure how to calculate the total length of the template, would I just add all the sides up together?

    and isn't the area of the square 36cm^2 ?
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  6. #6
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    can someone please show me how to calculate the total length , please. maths is not my best subject
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