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The question is:

If the area of a parallelogram $JKLM$ is $n$ and if length of $KN$ is $n+(1/n)$, then find the length of $JM$. (The answer is $n^2 /( n^2+1 )$.)

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How would i go about solving this problem ?

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    Do you know the formula for the area of a parallelogramm?2012-06-08
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    Formula is : lxW2012-06-08
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    And how are $l$ and $W$ in $l \times W$ expressed in terms of your points $K, L, J, N, M$=2012-06-08
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    I tried applying Pythagoras formula to triangle to obtain the hypotenuse. and then insert that value in area of parallelogram to obtain the other side but it doesn't work.2012-06-08
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    why would you need the hypotenuse? That's not in the area calculation anywhere.2012-06-08
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    I find the question rather strange: $n$ has the dimension of area, so what dimension does $n+1/n$ have? Nothing sensible, and certianly not length.2012-06-08
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    Thats a standardized test question .. A lot of their questions don't make any sense.2012-06-08

1 Answers 1

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The area of a parallelogram (or see on Wikipedia) is the base times the height. The base here is $JM$ and the height is $KN$, so the area is $$KN * JM = n$$

So you have

$$ \left(n + \frac{1}{n}\right)*JM = n $$ Then you solve for $JM$

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    I like this method.. How did you get the formula for the Area ? KN * JM (KN is the height) . Isnt the Area of a Prarallelogram L x W or ( JK x JM)2012-06-08
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    @Rajeshwar: It is the formula for the area of a parallelogram. You can for example see here: http://en.wikipedia.org/wiki/Parallelogram#Area_formulas2012-06-08
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    @Rajeshwar: So in general the area of a parallelogram is the base times height. Your base is $JM$, the height is $KM$, so the area is the product $JM*KN$.2012-06-08