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perl

  • 4 years ago

Maggie has a kite with the dimensions shown below. What is the width of the kite?

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  1. perl
    • 4 years ago
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    im not sure what theorem is used here

  2. perl
    • 4 years ago
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    whats up rooma

  3. perl
    • 4 years ago
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    rumoor

  4. Directrix
    • 4 years ago
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    |dw:1328862799911:dw|To find x, this theorem is used. If an altitude is drawn to the hypotenuse of a right triangle, the length of the altitude is the geometric mean between the lengths of the segments of the hypotenuse.

  5. Directrix
    • 4 years ago
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    11 is to x as x is to 25. 11/x = x/25 x^2 = 25*11 x = 5 √ 11

  6. Directrix
    • 4 years ago
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    The width of the kite is 2 times ( 5 √ 11 = 10 √ 11

  7. perl
    • 4 years ago
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    woops, didnt see that right angle there, yes makes sense now

  8. anonymous
    • 4 years ago
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    You don't need that theorem just use pyhtagoras theorem on the three triangles. If the remainng side lenghts are y and z. x^2+25^2=y^2 and x^2+11^2=z^2. and y^2+z^2=36^2. 2x^2+25^2+11^2=36^2.

  9. perl
    • 4 years ago
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    where are you getting y^2 + z^2 = 36^2

  10. perl
    • 4 years ago
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    oh i see, yes you can prove it that way

  11. perl
    • 4 years ago
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    so you actually proved the general result |dw:1328881279082:dw|

  12. perl
    • 4 years ago
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    and after doing some algebra we have h = sqrt (ab)

  13. perl
    • 4 years ago
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    so this geometric mean theorem falls out from pythagorean theorem

  14. radar
    • 4 years ago
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    Or properties of similar triangles (proportions) a:h :: h:b 11:h :: h:25 \[h ^{2}=11 X 25\]\[h = \sqrt{11X25}=5\sqrt{11}\]

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