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Math Help - Ratio

  1. #1
    Junior Member Dragon's Avatar
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    Ratio

    Find the Ratio of the area of the triangle DEC to the Area of the parallelogram ABCD

    When: AF is 1 FB is 2 BC is 2
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Dragon View Post
    Find the Ratio of the area of the triangle DEC to the Area of the parallelogram ABCD

    When: AF is 1 FB is 2 BC is 2
    Triangle DEC is similar to triangle BEF, (angle DEC = angle BEF as they are
    vertical angles, and angle EDC = angle FBE)

    So take DC and BF as the bases of these two triagles, they are in the ratio
    of 3:2 (given). Hence their heights are in the ratio 3:2, so the heights of
    triangle DEC and parallologram ABCD are in the ratio of 3:5


    Hence as the area of a triangle is base*height/2 and that of a
    parallellogram is base times height, and they share a common base the areas
    of the triangle and parallelogram are in the ratio 3/2:5 or 3:10.

    RonL
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