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Math Help - how to find the length of the diagonal in a parallelogram

  1. #1
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    how to find the length of the diagonal in a parallelogram

    when it is known that the lengths of the two adjacent sides of the parallelogram viz. 6 and 10, is it possible to find the length of the diagonal containing that.

    Any help.

    Thanks
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  2. #2
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    Re: how to find the length of the diagonal in a parallelogram

    Quote Originally Posted by arangu1508 View Post
    when it is known that the lengths of the two adjacent sides of the parallelogram viz. 6 and 10, is it possible to find the length of the diagonal containing that.

    Any help.

    Thanks
    According to the Law of Cosine we know that :

    d^2=a^2+b^2-2ab\cdot \cos \angle (a,b)

    So if you don't know angle between two sides of parallelogram you cannot calculate lengths of diagonals .
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  3. #3
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    Re: how to find the length of the diagonal in a parallelogram

    My original question is

    the vector sum of the forces of magnitude 10N and 6N can be

    (a) 2N (b) 8N (c) 10N and (d) 18N

    I thought the vector sum would be the diagonal of parallelogram.

    Then how to go about this sum.

    am I on the right track?

    Kindly guide me.
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  4. #4
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    Re: how to find the length of the diagonal in a parallelogram

    Quote Originally Posted by arangu1508 View Post
    My original question is

    the vector sum of the forces of magnitude 10N and 6N can be

    (a) 2N (b) 8N (c) 10N and (d) 18N

    I thought the vector sum would be the diagonal of parallelogram.

    Then how to go about this sum.

    am I on the right track?

    Kindly guide me.
    Hint: Use Triangle Inequality Theorem to eliminate solutions that are not possible...
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  5. #5
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    Re: how to find the length of the diagonal in a parallelogram

    I have gone through the link. Thank you. According to that except the option (a) 2N rest of the options are possible. Is it okay?

    Thank you Mr. Princeps
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  6. #6
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    Re: how to find the length of the diagonal in a parallelogram

    Quote Originally Posted by arangu1508 View Post
    I have gone through the link. Thank you. According to that except the option (a) 2N rest of the options are possible. Is it okay?

    Thank you Mr. Princeps
    Option (d) isn't possible also because 6 + 10 isn't greater than 18
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  7. #7
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    Re: how to find the length of the diagonal in a parallelogram

    Thank you for your guidance.
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