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Math Help - Need some measurements

  1. #1
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    Need some measurements

    Need some measurements-house-measurements.jpg

    Note that no measurements are equal in length with one another. Please find the measurement for the X's (which are all different lengths).
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Movies32 View Post
    Click image for larger version. 

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    Note that no measurements are equal in length with one another. Please find the measurement for the X's (which are all different lengths).
    Let's get some of these vertices labelled. I'm going to call the 3 "corners" across the top A B C from left to right, and along the bottom diagonal D E F. Additionally I will call the vertical unknown distance x, the leftmost unknown y, and the rightmost unknown z.

    Note that trapezoids ACFD and BCFE are similar, so the sides are in proportion to each other.

    Thus:
    (80 + 120)/120 = 210/z

    Solve for z. I get z = 126. Thus y + z = 210 gives y = 84.

    Again:
    (80 + 120)/120 = 90/x

    I get x = 54.

    -Dan
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    I need the areas for each box please.
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Movies32 View Post
    I need the areas for each box please.
    (Shrugs) Each area is a trapezoid. The area of a trapezoid is:
    A = (1/2)(b1 + b2)h
    where b1 and b2 are the parallel "bases" and h is the perpendicular distance between the bases (the "height"). As these are "right" trapezoids getting the height is easy. And you now have the measurements for each side.

    I get the area of trapezoid BCFE is 5040 and the area of trapezoid ACED is 5760.

    -Dan
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