Sponsored Ad:
See the top rated post in this thread. Click here

Results 1 to 4 of 4

Thread: Finding maximum and minimum of areas and perimeters

  1. #1
    Trying to make mom and pop proud
    Join Date
    Aug 2018
    Posts
    1
    Rep Power
    1


    Good post? Yes | No

    Finding maximum and minimum of areas and perimeters

    Sponsored Ad:
    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

  2. #2
    Trying to make mom and pop proud
    Join Date
    Aug 2018
    Posts
    1
    Rep Power
    1


    1 out of 1 members found this post helpful. Good post? Yes | No

    Re: Finding maximum and minimum of areas and perimeters

    Quote Originally Posted by pratikw View Post
    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.

  3. #3
    Trying to make mom and pop proud
    Join Date
    Feb 2019
    Posts
    10
    Rep Power
    1


    Good post? Yes | No

    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

  4. #4
    Trying to make mom and pop proud
    Join Date
    Mar 2019
    Posts
    1
    Rep Power
    1


    Good post? Yes | No

    Re: Finding maximum and minimum of areas and perimeters

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

Thread Information

Users Browsing this Thread

There are currently 1 users browsing this thread. (0 members and 1 guests)

Similar Threads

  1. Ratio perimeters
    By Jen1984 in forum GMAT Problem Solving
    Replies: 4
    Last Post: 11-20-2008, 06:20 AM
  2. Minimum/Maximum value of S
    By Queen09 in forum GMAT Problem Solving
    Replies: 3
    Last Post: 09-12-2008, 08:49 AM
  3. Maximum
    By Unna100 in forum GMAT Problem Solving
    Replies: 8
    Last Post: 03-12-2007, 07:29 AM
  4. Maximum Value
    By Da_Gr8_Mperor in forum GMAT Data Sufficiency
    Replies: 6
    Last Post: 06-04-2006, 07:27 PM
  5. Maximum Value
    By wakau in forum GMAT Problem Solving
    Replies: 2
    Last Post: 07-03-2005, 12:20 PM

Tags for this Thread

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •