Page 1 of 2 12 LastLast
Results 1 to 15 of 16
Like Tree2Thanks

Thread: Finding the area of a window

  1. #1
    Newbie
    Joined
    Aug 2018
    From
    Male
    Posts
    6

    Finding the area of a window

    Hello I have an assignment to do, and i need help in the last question of this assignment

    I am allowed to get help with this assignment but I need to prove that i can do the questions because after submitting the assignment and marking, the teacher would ask random students to come up to the board and do the questions
    Here I will attach the question


    Finding the area of a window-42378185_262160367767736_8152274048693305344_n.png

    I just cant get to connect the perimeter to the area
    Also fyi we never studied intergration and differentiation(Or calculus), some suggested me to use Calculus but since it wasnt taught to us yet, i shouldnt use it
    I am guessing I have to use an Algebric Equation here?
    Last edited by eobardrush; Sep 23rd 2018 at 06:22 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    From
    Brisbane
    Posts
    1,072
    Thanks
    316

    Re: Finding the area of a window

    Have you found the length of the slant side in terms of a and b?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Aug 2018
    From
    Male
    Posts
    6

    Re: Finding the area of a window

    Quote Originally Posted by Debsta View Post
    Have you found the length of the slant side in terms of a and b?
    I am honestly not sure how to do this one at all.the perimeter written there had me confused for a while now. I tried using the formula of area, using 1/2 bh and area of rectangle lb equal to 750, but one of my friends said that wont work since the value of "750" is the "Perimeter"
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Feb 2015
    From
    Ottawa Ontario
    Posts
    2,067
    Thanks
    410

    Re: Finding the area of a window

    The triangle is isosceles (of course).
    Assuming b is rectangle's width, then triangle's height = 2b.
    Let c = triangle's equal sides.
    Then c = sqrt(4b^2 + a^2/4) [1]

    So we have a + 2b + 2c = 750
    Substitute [1] to get: a + 2b + 2(4b^2 + a^2/4) = 750
    Leads to the quadratic 12b^2 + 3000b - 4ab + 1500a - 750^2 = 0
    Solving for b:
    b = (a - 750 + sqrt(a^2 - 6000a + 2250000)) / 6

    I used brute strength to get maximum area 33786.8 where:
    a = 231, b = 73.13, c = 186.37

    Is the solution given? If so, are my calculation ok?
    And perhaps Debsta can confirm...or tell me I'm wrong!!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Aug 2018
    From
    Male
    Posts
    6

    Re: Finding the area of a window

    Quote Originally Posted by DenisB View Post
    The triangle is isosceles (of course).
    Assuming b is rectangle's width, then triangle's height = 2b.
    Let c = triangle's equal sides.
    Then c = sqrt(4b^2 + a^2/4) [1]

    So we have a + 2b + 2c = 750
    Substitute [1] to get: a + 2b + 2(4b^2 + a^2/4) = 750
    Leads to the quadratic 12b^2 + 3000b - 4ab + 1500a - 750^2 = 0
    Solving for b:
    b = (a - 750 + sqrt(a^2 - 6000a + 2250000)) / 6

    I used brute strength to get maximum area 33786.8 where:
    a = 231, b = 73.13, c = 186.37

    Is the solution given? If so, are my calculation ok?
    And perhaps Debsta can confirm...or tell me I'm wrong!!
    Hello!
    Unfortunately she didnt give us the solution but a classmate of mine did the same method too upto the "maximum area" it seems
    He isnt sure if its correct or not tho but he did exactly like you did
    Wasnt sure what "max area" meant
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Oct 2009
    From
    Brisbane
    Posts
    1,072
    Thanks
    316

    Re: Finding the area of a window

    I'd say the "width" of the window is a not b.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Joined
    Oct 2009
    From
    Brisbane
    Posts
    1,072
    Thanks
    316

    Re: Finding the area of a window

    Let the height of the triangle be 2a. This leads to the slant being $\displaystyle \frac{\sqrt5}{2}a$


    So Perimeter = $\displaystyle 2* \frac{\sqrt5}{2}a + a + 2b = 750$


    This gives $\displaystyle b=\frac{750 - (\sqrt5+1)a}{2}$ … **


    Now Area of window = area of rectangle + area of triangle = $\displaystyle a*b + \frac{1}{2}a*2a = ab + a^2$


    Now sub in ** for b and you'll have the Area in terms of a only. It will be a quadratic expression in a.


    Graph (as it suggests in the question), it will be an "upside-down" parabola and find the maximum area ie the highest point on the graph.

    (I got max area of approx. 56884 when a=303.38. Check that by doing it yourself - I did it very quickly.)

    You also have to find b, so sub a=303.38 into **.
    Last edited by Debsta; Sep 23rd 2018 at 04:50 PM.
    Thanks from DenisB
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Joined
    Feb 2015
    From
    Ottawa Ontario
    Posts
    2,067
    Thanks
    410

    Re: Finding the area of a window

    Quote Originally Posted by Debsta View Post
    Let the height of the triangle be 2a. This leads to the slant being $\displaystyle \frac{\sqrt5}{2}a$
    Disagree. Should be slant = sqrt[(2a)^2 + (a/2)^2] = aSQRT(17) / 2

    Also, area of 56,884 is evidently impossible:
    if instead the 750 was the perimeter of a square,
    area = (750/4)^2 = 35556
    Last edited by DenisB; Sep 23rd 2018 at 07:33 PM.
    Thanks from Debsta
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor
    Joined
    Feb 2015
    From
    Ottawa Ontario
    Posts
    2,067
    Thanks
    410

    Re: Finding the area of a window

    Quote Originally Posted by Debsta View Post
    I'd say the "width" of the window is a not b.
    Why? If his classmate used b, then the class must have been told b was the width.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    MHF Contributor
    Joined
    Oct 2009
    From
    Brisbane
    Posts
    1,072
    Thanks
    316

    Re: Finding the area of a window

    Quote Originally Posted by DenisB View Post
    Why? If his classmate used b, then the class must have been told b was the width.
    No I think his classmate just made that assumption. The problem is so much more "do-able" if the width is a. We can't assume the diagram is drawn to scale.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    MHF Contributor
    Joined
    Oct 2009
    From
    Brisbane
    Posts
    1,072
    Thanks
    316

    Re: Finding the area of a window

    Quote Originally Posted by DenisB View Post
    Why? If his classmate used b, then the class must have been told b was the width.
    No I think his classmate just made that assumption. The problem is so much more "do-able" if the width is a. We can't assume the diagram is drawn to scale.
    Follow Math Help Forum on Facebook and Google+

  12. #12
    MHF Contributor
    Joined
    Oct 2009
    From
    Brisbane
    Posts
    1,072
    Thanks
    316

    Re: Finding the area of a window

    Quote Originally Posted by DenisB View Post
    Disagree. Should be slant = sqrt[(2a)^2 + (a/2)^2] = aSQRT(17) / 2

    Also, area of 56,884 is evidently impossible:
    if instead the 750 was the perimeter of a square,
    area = (750/4)^2 = 35556
    Yes you are correct. I made a dumb mistake when simplifying Pythagoras' rule.
    I'll leave it to eobardrush to fix it up from there.
    Last edited by Debsta; Sep 23rd 2018 at 08:07 PM.
    Follow Math Help Forum on Facebook and Google+

  13. #13
    MHF Contributor
    Joined
    Oct 2009
    From
    Brisbane
    Posts
    1,072
    Thanks
    316

    Re: Finding the area of a window

    Quote Originally Posted by Debsta View Post
    Let the height of the triangle be 2a. This leads to the slant being $\displaystyle \frac{\sqrt17}{2}a$


    So Perimeter = $\displaystyle 2* \frac{\sqrt17}{2}a + a + 2b = 750$


    This gives $\displaystyle b=\frac{750 - (\sqrt17+1)a}{2}$ … **


    Now Area of window = area of rectangle + area of triangle = $\displaystyle a*b + \frac{1}{2}a*2a = ab + a^2$


    Now sub in ** for b and you'll have the Area in terms of a only. It will be a quadratic expression in a.


    Graph (as it suggests in the question), it will be an "upside-down" parabola and find the maximum area ie the highest point on the graph.

    (I got max area of approx. 56884 when a=303.38. Check that by doing it yourself - I did it very quickly.) This is obviously not correct now.

    You also have to find b, so sub a=303.38 into **.
    Thanks Denis for pointing out my mistake. As they say "Two heads are better than one!"
    Follow Math Help Forum on Facebook and Google+

  14. #14
    MHF Contributor
    Joined
    Feb 2015
    From
    Ottawa Ontario
    Posts
    2,067
    Thanks
    410

    Re: Finding the area of a window

    Stinking(!) out loud: Debsta, do you see anything wrong with making the rectangle a square?
    That's since a square produces max. area...haven't tried it...too lazy!
    Follow Math Help Forum on Facebook and Google+

  15. #15
    MHF Contributor
    Joined
    Oct 2009
    From
    Brisbane
    Posts
    1,072
    Thanks
    316

    Re: Finding the area of a window

    Quote Originally Posted by DenisB View Post
    Stinking(!) out loud: Debsta, do you see anything wrong with making the rectangle a square?
    That's since a square produces max. area...haven't tried it...too lazy!
    No that wouldn't necessarily work, because the window is not just the rectangle.
    Follow Math Help Forum on Facebook and Google+

Page 1 of 2 12 LastLast

Similar Math Help Forum Discussions

  1. Maximizing the area of a window
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Aug 22nd 2016, 05:31 AM
  2. Area of a Window
    Posted in the Calculus Forum
    Replies: 4
    Last Post: Dec 2nd 2010, 06:08 PM
  3. Proof regarding a norman window max area...
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: Jun 28th 2010, 06:41 PM
  4. Finding the area..
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 13th 2010, 03:29 PM
  5. Replies: 3
    Last Post: Feb 8th 2009, 04:07 PM

/mathhelpforum @mathhelpforum