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

• January 9th 2012, 12:03 AM
arangu1508
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
• January 9th 2012, 12:22 AM
princeps
Re: how to find the length of the diagonal in a parallelogram
Quote:

Originally Posted by arangu1508
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 .
• January 9th 2012, 12:34 AM
arangu1508
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.

am I on the right track?

Kindly guide me.
• January 9th 2012, 12:56 AM
princeps
Re: how to find the length of the diagonal in a parallelogram
Quote:

Originally Posted by arangu1508
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.

am I on the right track?

Kindly guide me.

Hint: Use Triangle Inequality Theorem to eliminate solutions that are not possible...
• January 9th 2012, 01:26 AM
arangu1508
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
• January 9th 2012, 01:34 AM
princeps
Re: how to find the length of the diagonal in a parallelogram
Quote:

Originally Posted by arangu1508
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
• January 9th 2012, 02:45 AM
arangu1508
Re: how to find the length of the diagonal in a parallelogram