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Math Help - Geometrical Problem

  1. #1
    Member VitaX's Avatar
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    Geometrical Problem



    Figure here shows a rectangle inscribed in an isosceles right triangle whose hypotenuse is 2 units long.

    a. Express the y coordinate of P in terms of x. I get 1 - x ... Correct?
    b. Express the area of the rectangle in terms of x. Not sure how to go about solving this one.
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  2. #2
    Super Member Matt Westwood's Avatar
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    a) Correct.

    b) Area of rectangle is one side multiplied by the other.

    One of the sides is 2x as it's x one way from the origin and x the other way.

    You've already worked out the length of the other side. You did it in part a).
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  3. #3
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    earboth's Avatar
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    Quote Originally Posted by VitaX View Post


    Figure here shows a rectangle inscribed in an isosceles right triangle whose hypotenuse is 2 units long.

    a. Express the y coordinate of P in terms of x. I get 1 - x ... Correct? <<<<< Yes
    b. Express the area of the rectangle in terms of x. Not sure how to go about solving this one.
    The area of a rectangle is calculated by: A = length \cdot width

    With your problem the length = 2x
    and the width is w = 1 - x

    Plug in these terms into the formula above.
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  4. #4
    Member VitaX's Avatar
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    Quote Originally Posted by earboth View Post
    The area of a rectangle is calculated by: A = length \cdot width

    With your problem the length = 2x
    and the width is w = 1 - x

    Plug in these terms into the formula above.
    would the area be better expressed as 2x(1-x) units squared or 2x-2x^2 units squared.
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  5. #5
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    That really makes no difference, but if you want it to look neater then write 2x(1-x)
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