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Math Help - hexagon differences

  1. #1
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    Question hexagon differences

    I attached a file since the last time I tried to just show the pic it didn't go through. I think I start with
    P/T=4/5
    R/T=2/5
    How do I figure out the difference of n amd m?


    In the following figure, the similarity ratio of regular hexagon P to regular hexagon T is 4/5 and the similarity ratio of regular hexagon R to T is 2/5. What is the difference of n and m?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by sanee66 View Post
    I attached a file since the last time I tried to just show the pic it didn't go through. I think I start with
    P/T=4/5
    R/T=2/5
    How do I figure out the difference of n amd m?


    In the following figure, the similarity ratio of regular hexagon P to regular hexagon T is 4/5 and the similarity ratio of regular hexagon R to T is 2/5. What is the difference of n and m?
    Here's one way

    we have: \frac {P}{T} = \frac {4}{5}

    \Rightarrow T = \frac {5}{4} P ...................(1)

    we also have: \frac {R}{T} = \frac {2}{5}

    \Rightarrow  T = \frac {5}{2} R ...................(2)

    since (1) = (2) = T, we can equate the expressions.

    \Rightarrow \frac {5}{4} P = \frac {5}{2} R

    \Rightarrow P = 2R

    \Rightarrow m + 12 = 2(6) \implies \boxed { m = 0 }

    But we have that: T = \frac {5}{4} P

    \Rightarrow n - 4 = \frac {5}{4} \cdot 12 = 15 \implies \boxed { n = 19 }

    Thus, n - m = 19 - 0 = 19
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  3. #3
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    Hello, sanee!

    A slightly different approach . . .


    We have: . \frac{P}{T} = \frac{4}{5}\quad\Rightarrow\quad \frac{m+12}{n-4} = \frac{4}{5}\quad\Rightarrow\quad 5m \:=\:4n-76 . [1]

    We have: . \frac{R}{T} = \frac{2}{5}\quad\Rightarrow\quad\frac{6}{n-4} = \frac{2}{5}\quad\Rightarrow\quad\boxed{n = 19} . [2]


    Substitute [2] into [1]: . 5m \:=\:4(19) - 76\quad\Rightarrow\quad\boxed{m\,=\,0}


    Therefore: . n - m \;=\;19 - 0 \;=\;\boxed{\boxed{19}}

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