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A triangle has two sides of length 12 and 18. What is the smallest possible whole-number length for the third side?

1 Answer

3 votes

Answer:

7

Explanation:

You want the integer length of the shortest third side that will form a triangle with sides 12 and 18.

Triangle inequality

The triangle inequality requires the sum of any two sides exceed the measure of the third side. If x is the short side, we want ...

x +12 > 18

x > 6 . . . . . . subtract 12

The smallest integer greater than 6 is 7.

The third side must be at least 7 units long.

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Additional comment

Some authors write the triangle inequality as a+b≥c. If you use that version, then the shortest side can be 6 units. The resulting "triangle" will have zero area, and will look like a line segment 18 units long.

User Guillermo Prandi
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