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Thread: help with question

  1. #1
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    Post help with question

    1.A right triangle has an area of 25 cm^2. express the hypotenuse, h, of this triangle as a function of its perimeter, p

    2.Find |m|
    Root3(m+9)=3 + Root3(m-9)

    thanks for the help
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  2. #2
    Super Member

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    Hello, monkius!

    1.A right triangle has an area of 25 cm².
    Express the hypotenuse, $\displaystyle h$, of this triangle as a function of its perimeter, $\displaystyle p.$
    Code:
          *
          |  *    h
        b |     *
          |        *
          * - - - - - *
                a

    The area is 25 cm²: .$\displaystyle \frac{1}{2}ab = 25 \quad\Rightarrow\quad ab = 50$

    The perimeter is: .$\displaystyle p \:=\:a+b+h \quad\Rightarrow\quad a + b \:=\:p -h$ .[1]

    Square both sides of equation [1]: .$\displaystyle (a+b)^2 \:=\:(p-h)^2$

    And we have: .$\displaystyle a^2 + 2ab + b^2 \:=\:p^2 - 2 ph + h^2$

    . . or: .$\displaystyle \underbrace{(a^2+b^2)}_{\text{This is }h^2} \;+ \;2\underbrace{(ab)}_{\text{This is 50}} \:=\:p^2 - 2ph + h^2$

    So we have: .$\displaystyle h^2 + 100 \;=\;p^2 - 2ph + h^2 \quad\Rightarrow\quad 2ph \:=\:p^2-100$


    Therefore: .$\displaystyle \boxed{h \;=\;\frac{p^2-100}{2p} }$

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