Q.

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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a

5 < x < 29

b

12 < x < 29

c

12 < x < 17 

d

5 < x < 17

answer is D.

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Detailed Solution

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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=29cm.

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=15cm.

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