Final answer:The length of the third side of atrianglewith two given side lengths (5 and 12) must be greater than 7 and less than 17, according to the triangle inequality theorem. The Pythagorean theorem could provide possible lengths if the triangle was right, but these also need to satisfy the triangle inequality.Explanation:In Mathematics, when you are given thelengthsof two sides of a triangle, the length of the third side can fall into a certain range, not just a specific value. The range is determined by the triangle inequality theorem, which states that the length of any side of a triangle must be less than the sum of the other two sides and greater than the difference. In this case, with sides of lengths 5 and 12, the third side's length must be more than 7 (12-5) and less than 17 (12+5).Another important concept is thePythagorean theorem, which states: a² + b² = c². This theorem applies to right triangles, but since we don't know whether this triangle is a right triangle, we may speculate on right triangle scenarios. If the triangle were a right triangle, using the Pythagorean theorem could provide us other possible lengths, but it must still satisfy the triangle inequality theorem.Learn more about Triangle Side Length here:brainly.com/question/24273594#SPJ12...

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