Two sides of a triangle have side lengths of 17 meters and 12 meters. What is the possible length range for the third side?

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5 < x < 29

12 < x < 29

12 < x < 17

5 < x < 17

answer is D.

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Detailed Solution

Concept: Because the lengths of any two sides of a triangle must add up to more than the length of the third side.

Given that the two sides of the triangle are 12cm and 17cm.

As a result, the third side must be less than $12 + 17 = 29 c m .$

Furthermore, the third side cannot be less than the difference between the first two sides.

So, the third side must be greater than $17 - 12 = 15 c m$ .

As a result, the length of the third side should be greater than 5 cm but less than 29 cm.

So possible range = 5 < x< 29

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