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Math Help - Area of a Rectangle!! Help please!!!

  1. #1
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    Area of a Rectangle!! Help please!!!

    hey, so im trying to help my cousin with a math problem about finding the area of the rectangle. the problem says,

    A point P is in the first quadrant of a coordinate plane on the line y = 7 - 3x. From the point P perpendiculars are drawn from both the x and y-axis. what is the largest possible area of the rectangle.

    the answer in the book says 49/12 but could you help me out and show how its done thanks. sorry i dont have a graph on here

    mathlete
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  2. #2
    Eater of Worlds
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    I assume you drew the triangle and rectangle just to get a picture?.

    The width of the rectangle is x and the height is y.

    The area of the rectangle is A=xy.

    We know y=-3x+7

    So, the area is A=x(-3x+7)=-3x^{2}+7x

    Now, by calc or x=\frac{-b}{2a}, we can solve for x.

    a=-3, \;\ b=7

    \frac{-7}{2(-3)}=\frac{7}{6} is the width.

    Plug this into y to find the height.

    Then multiply the two answers to get the area. I bet you get 49/12.
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