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two sides of a triangle measure 10cm and 15cm. which of the following is long enought to be the measure of the third side. 1cm, 3cm, 4cm, or 6cm

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The sum of the two shorter sides must be longer than the longest side. The answer would be 6cm.
For sides of a triangle to be "true", the two shortest sides must be greater than the third side. In other words, 10 plus another number must be greater than 15.

10+1 > 15 (no, 11<15)
10+3 > 15 (no, 13<15)
10+4 > 15 (no, 14<15)
10+6 > 15 (yes, 16>15)

Therefore, the missing side length is 6cm.

:)

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