Question 1012965
i have a problem with this problem and the problem is this.


you haven't defined what kind of parallelogram you are dealing with.
this means that you can have several different kinds of parallelograms where the area is 2000 and the perimeter is 240.


let me explain.


area of a paraallelogram is base * height = area.


since the area is 2000, you get base * height = 2000.


perimeter of a parallelogram is 2 * base + 2 * side = perimeter.


since the perimeter is 240, you get 2 * base + 2 * side = 240.


you are dealing with 2 equations and 3 variables, so you won't get one answer.


the best you will be able to do is get one answer based on an assumption in the value of one of the other variables.


since both equations have the same base in them, we can relate these equations in terms of the base.


from the first equation, we get base = 2000 / height.


from the second equation, we get base = 120 - side.


if we substgitute 2000 / height for base in the second equation, we get:


2000 / height = 120 - side.


if we solve this equation for side, we get side = 120 - 2000 / height.


now let's look at some values that will satisfy both requirements.


the first requirement is that the area is equal to 2000.
the second requirement is that the perimeter is equal to 240.


we will assume a height and we will then calculate the base and the side.


we will work from the following two equations.


base = 2000 / height.


side = 120 - 2000 / height.


so, we'll take some values for height and then calculate base and side and then see if the requirements of the problem are satisfied.


the following excel printout shows you what happens for values of height from 0 to 240.


see below the printout for more comments.


<img src = "http://theo.x10hosting.com/2016/011001.jpg" alt="%%%" </>


what you see from this printout is that all of the heights given and sides and bases calculated give you a parallelogram that has an area of 2000 and a perimeter of 240.


the 2 parallelograms that are rectangles have been marked.
these are the ones where the height is equal to the side.


the other parallelograms are not rectangles, but have some angles other than 90 degrees.
these are the ones where the height is not equal to the side.


they all, however, give you an area of 2000 and a perimeter of 240.


your question was to find the length of the long and short diagonals.


you will get several answers depending on which of these possible parallelograms is the one that you want to calculate the diagonals from.


if you meant rectangle, you will get one answer.


in other words, something is missing in the specification of the problem.


if you had given the height, then the others could have been worked out.
if you had given the length of a side, then the others could have been worked out.


as the problem is specified, one solution is not possible.


i could be wrong, but that's my belief based on my analysis shown above.