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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?

### 2 Answers

Relevance
• 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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