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tmua.me Medium Set E Paper 2 · Q2

Paper 2Logic & proofGeometry

Consider the following claim about positive numbers aa, bb and cc:

If aa, bb and cc are the side lengths of a triangle, then a2a^2, b2b^2 and c2c^2 are also the side lengths of a triangle.

Here a triangle must have three non-collinear vertices. Which of the following is a counterexample?

Aa=1,b=2,c=3a=1,\quad b=2,\quad c=3
Ba=2,b=3,c=3a=2,\quad b=3,\quad c=3
Ca=3,b=3,c=4a=3,\quad b=3,\quad c=4
Da=2,b=3,c=4a=2,\quad b=3,\quad c=4
Ea=1,b=2,c=4a=1,\quad b=2,\quad c=4

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