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12. A triangle has side lengths of 13 inches and 35 inches. What are the possible sidelengths for the third side of the triangle? Is a side length of 4 feet possible? Why or why not?​

User Ali Ahmad
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1 Answer

12 votes

Answer:

22 in < third side < 48 inches

48 inches is not a possible side length

Explanation:

The triangle inequality allows the third side to range between the difference and the sum of the two given sides:

(35 -13) < s < (35 +13)

22 < s < 48 . . . . . . inches

A side length of 4 feet (48 inches) does not satisfy the triangle inequality.

_____

Additional comment

Some authors allow the "or equal to" case in the triangle inequality. When the sum of the shortest sides is equal to the longest side, the triangle looks like a line segment: it has an area of zero. Other authors prefer a strict inequality, so the triangle has non-zero area. That is the version we have used to answer this question. YMMV

User Anarhikos
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