PSAT Math : How to find the length of the side of an acute / obtuse triangle

Study concepts, example questions & explanations for PSAT Math

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Example Questions

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Example Question #561 : Geometry

All of the following could be the possible side lengths of a triangle EXCEPT:

Possible Answers:

Correct answer:

Explanation:

The length of the third side of a triangle must always be between (but not equal to) the sum and the difference of the other two sides. 

For instance, take the example of 2, 6, and 7.

 and . Therefore, the third side length must be greater than 4 and less than 8. Because 7 is greater than 4 and less than 8, it is possible for these to be the side lengths of a triangle.

The 5, 7, 12 answer choice is the only option for which this is not the case.

 and . Therefore, the third side length must be between 2 and 12. Because it is equal to the sum, not less than the sum, it is not possible that these could be the side lengths of a triangle.

 

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