A triangle has sides measuring 5 inches and 8 inches. If x represents the length in inches of the third side, which inequality gives the range of possible values for x?A.5 ≤ x ≤ 8B.5 < x < 8C.3 < x < 13D.3 ≤ x ≤ 13
Question
A triangle has sides measuring 5 inches and 8 inches. If x represents the length in inches of the third side, which inequality gives the range of possible values for x?A.5 ≤ x ≤ 8B.5 < x < 8C.3 < x < 13D.3 ≤ x ≤ 13
Solution
The answer is D. 3 < x < 13.
This is because of the triangle inequality theorem, which states that the length of any side of a triangle must be less than the sum of the lengths of the other two sides, but more than the absolute difference of the lengths of the other two sides.
So, in this case, the third side must be less than 5 + 8 = 13 inches and more than |5 - 8| = 3 inches. Therefore, the range of possible values for x is 3 < x < 13.
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