The lengths of the two sides of a triangle are 12cm and 15cm. between what two measures should the length of the third side fall?

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The length of the third side will be less than 27 cm but larger than 3 cm

6 cm and less than 46 cm

4 cm and less than 66 cm

8 cm and less than 86 cm

answer is A.

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Detailed Solution

Concept: The triangle inequality theorem states that the sum of the lengths of two sides of a triangle is always higher than the length of the third side.
The sum and difference of these two sides will be determined.
The sides of a triangle are 12 cm and 15 cm long.
Remember that the third side should be less than their total but bigger than their difference.
The sum and difference of these two sides will be determined.
As a result, the third side will be shorter than the total of the first two sides (12 cm + 15 cm = 27 cm).
It will also be bigger than the difference between these two sides (15 cm - 12 cm = 3 cm).
As a result, the length of the third side will be less than 27 cm but larger than 3 cm.
Hence the correct answer is option number (1).

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