# Area of Square - Comparing squares

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 $n^2 /( n^2+1 )$.)

How would i go about solving this problem ?

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Do you know the formula for the area of a parallelogramm? –  Phira Jun 8 '12 at 14:51
Formula is : lxW –  Rajeshwar Jun 8 '12 at 14:54
And how are $l$ and $W$ in $l \times W$ expressed in terms of your points $K, L, J, N, M$= –  martini Jun 8 '12 at 14:55
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. –  Rajeshwar Jun 8 '12 at 14:55
why would you need the hypotenuse? That's not in the area calculation anywhere. –  Robert Mastragostino Jun 8 '12 at 15:05

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) –  Rajeshwar Jun 8 '12 at 15:11
@Rajeshwar: It is the formula for the area of a parallelogram. You can for example see here: en.wikipedia.org/wiki/Parallelogram#Area_formulas –  Thomas Jun 8 '12 at 15:13
@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 $JM*KN$. –  Thomas Jun 8 '12 at 15:14