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Ledah

  • 3 years ago

Two regular decagons have areas of 30 mm² and x² + 7x mm². What values of x make the decagons congruent?

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  1. apoorvk
    • 3 years ago
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    Since the areas are equal, equate the expressions for both areas: \[30 = x^2 + 7x\] Now, bring every term to the same side, and lo! you have a quadratic. solve it, find 'x' and enjoy!

  2. FoolAroundMath
    • 3 years ago
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    Two polygons are congruent if they are exactly the same. What can you say about the area of two congruent polygons?

  3. Ledah
    • 3 years ago
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    They should also be the same

  4. FoolAroundMath
    • 3 years ago
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    So, all you have to do is equate their areas and get a quadratic equation as obtained by @apoorvk and solve it.

  5. Ledah
    • 3 years ago
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    I got 5 and -6 as an answer.. I'm not sure if its right I'm still checking my work

  6. apoorvk
    • 3 years ago
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    Umm, sorry that isn't correct - did you split the middle term and factorize it?

  7. FoolAroundMath
    • 3 years ago
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    \(x=5\) does not satisfy the equation. What you have is \(x^{2}+7x-30 = 0\) Can you factorise the left hand side?

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