Question

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

third side be? Check all that apply.
A. 8
B. 5
D.2
-
E
19
-
F. 24

Answer 1

THE CORRECT ANSWER IS 10, PLEASE DO NOT CHOOSE 8, IT WAS WRONG FOR ME SO THE CORRECT ANSWER IS 10

Explanation:

Answer 2

A. 8

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.

_____

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.