Problem 10 · 2018 Math Kangaroo
Easy
Geometry & Measurement
area-fraction
The square ABCD has side length 3 cm. The points M and N, which lie on the sides AD and AB respectively, are joined to the corner C. That way the square is split into three parts of equal area. How long is the line segment DM?
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Answer: D — 2 cm
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Hint 1 of 2
Each of the three pieces has area equal to one third of the square.
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Hint 2 of 2
Triangle DMC has base DM and height DC = 3; set its area equal to a third of the square.
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Approach: use the equal-area condition on triangle DMC
- The square has area 9 cm², so each part has area 3 cm².
- Triangle DMC has area ½ · DM · DC = ½ · DM · 3 = 3, so DM = 2 cm.
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