What is the maximum possible area of a parallelogram with one side of length 2 meters and a perimeter of 24 meters?
The perimeter = 2*2 + 2x = 24 --> x = 10.
The are is maximized if the parallelogram is a rectangle, thus the maximum area is 2*10 = 20.
In this question I have one query that as per the Theory learnt - Max. possible Area with a given perimeter is a SQUARE, so why here it is RECTANGLE?
Pls help with an explanation.
You are right in your understanding that the maximum possible area for a given perimeter is a square.
So for a give perimeter of 24, the sides should have been 24/4 = 6 units each.
But here we have an additional
constraint that the length of one of the sides is 2.
Now, if the other sides are also 2 each, the perimeter will only be 8 and not 24.
So the only way to have a perimeter of 24 and
length of one of the sides as 2 is to take the parallelogram as a rectangle, which will result in the answer explained in the posts above.