# Thread: Finding maximum and minimum of areas and perimeters

1. ## Finding maximum and minimum of areas and perimeters

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  Reply With Quote

2. ## 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.

Hope this helps.

Thanks.  Reply With Quote

3. ## Re: Finding maximum and minimum of areas and perimeters

Let's say that perpendicular of the given right triangle is x, then the base is (40-x)
Area of given right triangle will be = (1/2)*(x)*(40-x)

You can try this for x = 5, 10, 15, 20 which will have same area value of triangle for x = 35, 30, 25, 20 respectively
Out of the four options, at x=20 we'll have the max area of triangle.

x=5, Area = 87.5
x=10, Area = 150
x=15, Area = 187.5
x=20, Area = 200  Reply With Quote

4. ## Re: Finding maximum and minimum of areas and perimeters

Both the answers were useful and unique in their own ways.  Reply With Quote

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concept, geometry, geometry question gre, maximum, triangle 