Problem 9 · 2012 Math Kangaroo
Medium
Geometry & Measurement
area
The quadrilateral ABCD with side length 4 cm has the same area as triangle ECD. What is the perpendicular distance from point E to the line g?
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Answer: C — 12 cm
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Hint 1 of 2
Find the height of triangle ECD using its known area and base CD.
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Hint 2 of 2
Line g is the far side of the square, one square-width past CD.
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Approach: back out a length from the equal-area condition
- The square has side 4, so its area is 16; triangle ECD has the same area, 16.
- Taking CD (length 4) as the base, its area gives ½ · 4 · h = 16, so the distance from E to the line CD is h = 8.
- Line g is the opposite side of the square, a further 4 cm beyond CD, and E is on the far side, so the distance from E to g is 8 + 4 = 12 cm (C).
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