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Re: Finding maximum and minimum of areas and perimeters
Originally Posted by
pratikw
I stumbled upon these questions in Manhattan series, where we are supposed to find the maximum and minimum areas and perimeters of the polygons.
There are these questions, that i am not able to solve, I have thoroughly read the concept yet I am facing difficulty because I am still getting confused with the concept.
1. The lengths of the two shorter legs of a right triangle add up to 40 units.
2. What is the maximum possible area of the triangle?
Can somebody please explain me this concept
Hi,
For any given perimeter, generally equilateral polygon (a polygon with all sides equal) will have maximum area.
For example, for a given perimeter of a triangle equilateral triangle will have maximum area.
But, in the above question we have a right angle triangle, hence it can't be an equilateral triangle.
So, next best we can make an isosceles triangle.
Given: a+b = 40 for an isosceles right traingle a = b => 2a = 40 => a = 20 = b
Area of traingle= 1/2*a*b = 1/2*20*20 = 200 units.
Required answer is 200 units.
Hope this helps.
Thanks.