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Math Help - surds

  1. #1
    Member GAdams's Avatar
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    surds

    Two rectangles have equal area.

    The length of the first is (root2-10) and the width is the same.

    The second rectangle has width root3.

    Find the length of the second rectangle. Give the answer is the form p(root3).

    I tried:

    calling the unknown side x...

    (root10 - 2) (root10 - 2) = root3 (x)



    10 - 4root10 + 4 = root3 (x)

    ...but can't see how to find answer. Help!

    PS how do I show square root using latex?
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  2. #2
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    Combine the like terms on the left-hand side, and then divide through by the square root of three.
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  3. #3
    Member GAdams's Avatar
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    got as far as...

    14 - 4root30 = x
    ---------------
    3

    ....not sure from here
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  4. #4
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    What is it?
    is it \sqrt{2}-10 or \sqrt{10}-2?

    here is the link you need: http://www.mathhelpforum.com/math-he...-tutorial.html
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  5. #5
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    Quote Originally Posted by GAdams View Post
    Two rectangles have equal area.

    The length of the first is (root2-10) and the width is the same.

    The second rectangle has width root3.

    Find the length of the second rectangle. Give the answer is the form p(root3).

    I tried:

    calling the unknown side x...

    (root10 - 2) (root10 - 2) = root3 (x)



    10 - 4root10 + 4 = root3 (x)

    ...but can't see how to find answer. Help!

    PS how do I show square root using latex?
    A_1 = (\sqrt{2}-10)^2 = 102-20\sqrt{2}

    A_2 = A_1 = x\sqrt{3}

    \therefore 102-20\sqrt{2} = x\sqrt{3}

    x = \frac{102-20\sqrt2}{\sqrt3} = \frac{102\sqrt3-20\sqrt6}{3}

    I multiplied both sides by \frac{\sqrt{3}}{\sqrt3} in order to give a rational denominator as this is the convention
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  6. #6
    Member GAdams's Avatar
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    Quote Originally Posted by BabyMilo View Post
    What is it?
    is it \sqrt{2}-10 or \sqrt{10}-2?

    here is the link you need: http://www.mathhelpforum.com/math-he...-tutorial.html

    sorry!
    it's (\sqrt10 - 2) for each side of the first rectangle
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  7. #7
    Member GAdams's Avatar
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    (\sqrt10 -2) (\sqrt10 - 2) = \sqrt3 (x)

    10 -4\sqrt10 + 4 = \sqrt3 (x)

    14 - 4\sqrt10 = \sqrt3 (x)

    \frac{14 - 4\sqrt10}{\sqrt3} = x

    multiplying the left by \sqrt3 to rationalise the surd fraction gives this:

    \frac{14 - 4\sqrt10\sqrt3}{3} = x


    ...not sure from here
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