1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Minimization Problem

  1. Oct 11, 2009 #1
    1. The problem statement, all variables and given/known data

    The line joining P and Q crosses two parallel lines that are 8 units apart (thus, if I drew a vertical line from the top line to the bottom line, that would equal eight). The point R is 10 units from point P (as shown). How far from point Q should the point S be chosen so that the sum of the areas of the two triangles is at a minimum?


    2. Relevant equations

    [tex]Area = \frac{1}{2}bh[/tex]

    3. The attempt at a solution

    Okay ... not so bad, I think I know some of the steps.

    [tex]Area of 2 Triangles = \frac{1}{2}bh + \frac{1}{2}(b_{1})(h_{1})[/tex]

    b1 and h1 are just the base/height of the other trianglw (the one with points S and Q).

    So should I substitute 10 in for b and then do implicit differentiation? And how do I include the "8" that's here? Have something like height x and height 8-x for the two triangles?
  2. jcsd
  3. Oct 12, 2009 #2


    User Avatar
    Homework Helper

    you need to find the areas of the triangles in terms of the distance QS = s, before you can differentiate with respect to s to find your minima

    are you sure this is everything in the question 7 how its was given? unless it comes out as a really nice result (unlikely), I think you need to know the position of Q relative to R & P first
  4. Oct 12, 2009 #3
    Yes, I coped it directly from my book.

    So when doing this problem, how can I first find the areas in terms of QS? Should I just assign a variable to QS?
  5. Oct 12, 2009 #4


    User Avatar
    Homework Helper

    yeah, so find a way to write the area in terms of s = QS,

    expanding qhat you previously wrote, including the dependence on s
    [tex]A_{total}(s) = A_1(s) + A_2(s) = \frac{1}{2}b_1(s)h_1(s) + \frac{1}{2}b_{2}h_{2}(s)[/tex]
    only the base PR = b2, is independent of s

    however unless i'm missing something I still can't see how you can do this without something pinning the location of Q
  6. Oct 12, 2009 #5


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I think you have enough. Notice the two triangles will be similar
  7. Oct 12, 2009 #6


    User Avatar
    Homework Helper

    knew i was missing something easy - nice, (can't believe i missed it)
    so DMOC, its all about ratios of length
    Last edited: Oct 12, 2009
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook