Problem 14 · 2020 Math Kangaroo
Stretch
Geometry & Measurement
caseworksum-constraint
Two isosceles triangles that are not similar have at least one side of 20 cm and have equal perimeters. If one of them has a side of 8 cm, which of the following measures can be the measure of one side of the other triangle?
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Answer: D — 14 cm
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Hint 1 of 2
Build the two isosceles triangles so their perimeters match, with a 20 in one and an 8 in the other.
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Hint 2 of 2
Check that a candidate side length lets you form a genuine (non-degenerate, non-similar) triangle.
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Approach: construct matching-perimeter isosceles triangles and test a side
- Take (8, 20, 20): isosceles, perimeter 48, with sides 8 and 20.
- The other triangle (14, 14, 20) is isosceles, perimeter 48, and not similar to the first.
- It has a side of 14, so 14 cm is possible.
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