Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    1
    ReputationRep:
    Hi all,

    How would I go about answering question 7 part ii?

    Thanks
    Attached Images
     
    Offline

    15
    ReputationRep:
    If you have a rectangle with side lengths  x and  y say, then the perimeter,  P is given as  2(x+y) , and the area is 100 but the area is also given by  xy so  xy=100 . Can you think of where to go from there?
    Offline

    5
    ReputationRep:
    You can pose a rectangle of dimensions x and y, whose area is x \cdot y = 100 m^2.
    It's perimeter is equal to 2 \cdot (x+y).
    Hint:
    Spoiler:
    Show
    Using those formulas, you have to define the perimeter with respect to one side, with the constraint of the area.
    You then derive that expression of the perimeter, and find the turning point. Given the context, it will be a local minimum.
    • Thread Starter
    Offline

    1
    ReputationRep:
    The only thing I can think of is to differentiate the area and then put it into the perimeter equation ??
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by MartyO)
    You can pose a rectangle of dimensions x and y, whose area is x \cdot y = 100 m^2.
    It's perimeter is equal to 2 \cdot (x+y).
    Hint:
    Spoiler:
    Show
    Using those formulas, you have to define the perimeter with respect to one side, with the constraint of the area.
    You then derive that expression of the perimeter, and find the turning point. Given the context, it will be a local minimum.
    Is x equal to +/- 10?

    Ok so I did y=100/x from the area equation. Then I subbed it into the perimeter equation and differentiated and solved for x by putting it equal to zero. I got x=+/- 10 . However, if i sub that x into the area equation I get y also equals 10 which doesnt make sense if its a rectangle
    Offline

    15
    ReputationRep:
    (Original post by Olive123)
    Is x equal to +/- 10?
    x>0 since it represents length. So the rectangle is in fact a square. In fact for any rectangle,the rectangle will have greatest perimeter for any given area if and only if it is a square.
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by B_9710)
    x>0 since it represents length. So the rectangle is in fact a square. In fact for any rectangle,the rectangle will have greatest perimeter for any given area if and only if it is a square.
    So is my answer wrong ?

    How can a rectangle be a square ?
    Offline

    15
    ReputationRep:
    (Original post by Olive123)
    So is my answer wrong ?

    How can a rectangle be a square ?
    All rectangles are squares, just like all rectangles are parallelograms.
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by B_9710)
    All rectangles are squares, just like all rectangles are parallelograms.
    Ahh right (you learn something new everyday ) thanks haha

    so would the dimensions be 10 by 10 then ?
    Offline

    15
    ReputationRep:
    (Original post by Olive123)
    Ahh right (you learn something new everyday ) thanks haha

    so would the dimensions be 10 by 10 then ?
    Yes.
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by B_9710)
    Yes.
    Thank you sooooooo much
    • Study Helper
    Offline

    16
    ReputationRep:
    Study Helper
    (Original post by B_9710)
    All rectangles are squares, just like all rectangles are parallelograms.
    I think you mean "all squares are rectangles" - I can think of plenty of rectangles that aren't squares!

    (Original post by Olive123)
    Ahh right (you learn something new everyday ) thanks haha

    so would the dimensions be 10 by 10 then ?
    As above, a square is just a special case of a rectangle in which all the sides are equal.
    Offline

    15
    ReputationRep:
    (Original post by davros)
    I think you mean "all squares are rectangles" - I can think of plenty of rectangles that aren't squares!
    Of course mate, got my words mixed up.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Has a teacher ever helped you cheat?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Write a reply...
    Reply
    Hide
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.