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What is the height (x) of the trapezium ABDE?

An isosceles triangle ABC is cut horizontally at a height of 10 cm from its vertex to form a trapezium ABDE.

The base of triangle ABC was 9 cm. 

The length DE of the trapezium is 6 cm.

What is the height (x) of the trapezium ABDE?

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2 Answers

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  • User
    Lv 7
    1 month ago

    Look at the "top" triangle (that is cut off).

    It has a height of 10 and a base of 6.

    The "full" triangle is

    the very same sort of triangle, same angles.

    In other words: similar triangles.

    SO

    we can use the ratio of the smaller (top) triangle to the full triangle

    to find the total height.

    BaseFull/BaseTop = HeightFull/HeightTop

    9/6 = HFull/10

    HFull = 15

    since the top triangle is 10 cm high

    the base trapezoid must be 5 cm high

  • Pope
    Lv 7
    1 month ago

    10 : (10 + x) = 6 : 9

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