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anonymous

  • one year ago

Find the length of a side of rhombus ABCD if AE=6".

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  1. anonymous
    • one year ago
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    |dw:1437452607189:dw|

  2. mathstudent55
    • one year ago
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    What do you know about the diagonals of a rhombus?

  3. anonymous
    • one year ago
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    AD=12"

  4. anonymous
    • one year ago
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    CB=2x

  5. mathstudent55
    • one year ago
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    Yes, the diagonals of a rhombus bisect each other, but there is another important property of the diagonals of a rhombus.

  6. anonymous
    • one year ago
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    What is the other property?

  7. mathstudent55
    • one year ago
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    The are perpendicular to each other.

  8. mathstudent55
    • one year ago
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    Also, all sides of a rhombus are congruent. |dw:1437453036000:dw|

  9. mathstudent55
    • one year ago
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    Now you can use the Pythagorean theorem to find x.

  10. anonymous
    • one year ago
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    a^2+b^2=c^2. So, 2x^2-6^2=x^2.

  11. mathstudent55
    • one year ago
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    Yes, you have the right idea, but you need to be careful when you write it.

  12. mathstudent55
    • one year ago
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    \((2x)^2 - 6^2 = x^2\) The parentheses are important because you will get 4x^2. Without parentheses you have 2x^2 which is incorrect.

  13. mathstudent55
    • one year ago
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    I'd start with \(x^2 + 6^2 = (2x)^2\) Then change it to: \((2x)^2 - x^2 = 6^2\) Now continue from there.

  14. mathstudent55
    • one year ago
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    Did you get an answer?

  15. anonymous
    • one year ago
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    9

  16. mathstudent55
    • one year ago
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    ???

  17. mathstudent55
    • one year ago
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    The next step is \(4x^2 - x^2 = 36\) \(3x^2 = 36\) Divide both sides by 3 and then take the square root.

  18. anonymous
    • one year ago
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    oh opps i did something else

  19. anonymous
    • one year ago
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    x^2=12. So, x=3.4641016

  20. mathstudent55
    • one year ago
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    No don't find a decimal approximation. \(x^2 = 12\) \(x = \sqrt {12}\) \(x = \sqrt {4 \times 3} \) \(x = 2\sqrt 3\) Now we have x. The side of the rhombus is 2x, so multiply x by 2.

  21. anonymous
    • one year ago
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    Side= \[4\sqrt{3}\approx6.93\]

  22. anonymous
    • one year ago
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    I understand now. Thanks for the help @mathstudent55 :D Much appreciated.

  23. mathstudent55
    • one year ago
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    Excellent work! You're welcome.

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