Problem 22 · 2020 Math Kangaroo
Stretch
Geometry & Measurement
areaarea-fraction
A little kangaroo draws a line through the point P of the grid and then shades three triangles black, as shown. The areas of these triangles are proportional to which numbers?
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Answer: A — 1 : 4 : 9
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Hint 1 of 2
The three black triangles are similar to each other.
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Hint 2 of 2
Their linear sizes grow as 1, 2, 3 along the line.
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Approach: similar triangles with linear scale 1:2:3
- Each black triangle is cut off by the same line in a grid cell, so they are all similar.
- Their corresponding sides grow in the ratio 1 : 2 : 3 as you move along the line.
- Areas scale as the square of the sides, giving 1 : 4 : 9.
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