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

enter image description here

How would i go about solving this problem ?

  • 1
    $\begingroup$ Do you know the formula for the area of a parallelogramm? $\endgroup$ – Phira Jun 8 '12 at 14:51
  • $\begingroup$ Formula is : lxW $\endgroup$ – Rajeshwar Jun 8 '12 at 14:54
  • $\begingroup$ And how are $l$ and $W$ in $l \times W$ expressed in terms of your points $K, L, J, N, M$= $\endgroup$ – martini Jun 8 '12 at 14:55
  • $\begingroup$ 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. $\endgroup$ – Rajeshwar Jun 8 '12 at 14:55
  • $\begingroup$ why would you need the hypotenuse? That's not in the area calculation anywhere. $\endgroup$ – 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 $JM$

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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.