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Math Help - [SOLVED] Simple Co-Ordinate Geometry

  1. #1
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    Cool [SOLVED] Simple Co-Ordinate Geometry



    To find the area of triangle ABC I found out magnitudes of AB and CM then used the formula 1/2 x Base x Height as following:

    1/2 x under root 52 x under root 13

    The answer I get is 5.41 when solved with the calculator. But the correct answer is 13.

    I know that to get 13 square units as an answer we have to rationalize under root 52 into 2 under root 13 and then solve like this:

    1/2 x 2 (under root 13 ) x under root 13

    Then we cancel out 1/2 with 2 and multiple under root 13 with under root 13 to get under root 13 square. Then square cancels the under root and we get 13.

    What I want to know is that why is it like this? Why don't we get the same answer when solved directly through a canculator? How are we supposed to know whether to rationalize such numbers or to solve them with a calculator?

    Thanks.
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  2. #2
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    Hello unstopabl3
    Quote Originally Posted by unstopabl3 View Post

    To find the area of triangle ABC I found out magnitudes of AB and CM then used the formula 1/2 x Base x Height as following:

    1/2 x under root 52 x under root 13

    The answer I get is 5.41 when solved with the calculator. But the correct answer is 13.

    I know that to get 13 square units as an answer we have to rationalize under root 52 into 2 under root 13 and then solve like this:

    1/2 x 2 (under root 13 ) x under root 13

    Then we cancel out 1/2 with 2 and multiple under root 13 with under root 13 to get under root 13 square. Then square cancels the under root and we get 13.

    What I want to know is that why is it like this? Why don't we get the same answer when solved directly through a canculator? How are we supposed to know whether to rationalize such numbers or to solve them with a calculator?

    Thanks.
    You don't tell us where the point C is, but I think you want an explanation of why:
    \tfrac12\sqrt{52}\sqrt{13} = 13
    I think you have explained it perfectly well (although I don't really understand your use of the word 'under').
    \sqrt{52}=\sqrt{4\times13} = \sqrt4\times\sqrt{13} = 2\sqrt{13}
    Hence:
    \tfrac12\sqrt{52}\sqrt{13}= \tfrac12\times2\sqrt{13}\sqrt{13} = 13
    I can't explain why you got 5.41 on a calculator. Do it again. The answer is 13.

    When do you rationalise and when do you use a calculator? The answer is that you should attempt to rationalise every time - only reaching for a calculator as a last resort!

    Grandad
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  3. #3
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    Cool

    Thanks, we have to find the point C ourselves, although I should have mentioned it's co-ordinates but I forgot, so sorry about that.

    I don't know what came over me I was adding the square root of 52 and 13 instead of multiplying them

    I am used to calling sqr root as 'under root 13 or under root 52', you can say it's sort of a slang, sorry about that as well.

    Thanks for your help and advice
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