Question

A triangle has two sides of lengths 5 and 13. What value could the length of the

Answer 1

Answer:

  A. 8

Step-by-step explanation:

The length of the remaining side will be between the sum and difference of the given sides:

  5 + 13 = 18 . . . . upper limit of 3rd side length

  13 - 5 = 8 . . . . . lower limit of 3rd side length

The only answer choice in this range is 8.

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Comment on question and answers

Please note that this would not be an allowed answer for some triangle inequality questions. Some authors insist that the sum of the two shortest sides be greater than the longest side, so the triangle has non-zero area. Other authors allow the sum to be greater than or equal to the longest side. The only viable answer choice here is one that makes use of the "or equal to" condition. The 5-8-13 triangle will look like a line segment of length 13. It will have no area.