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Write an inequality to show the range of possible lengths for the third side of a triangle with sides 12 and 8

User Gongarek
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1 Answer

6 votes

Answer:

4 < s < 20

Explanation:

The triangle inequality requires that any side of a triangle must have a length that is between the difference and the sum of the lengths of the other two sides.

For unknown side s, the length must be ...

(12 -8) < s < (12 +8)

4 < x < 20

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Additional comment

The triangle inequality is usually written ...

a + b > c . . . . . for any assignment a, b, c to side lengths

If s is not the longest side, then we require ...

s +8 > 12 ⇒ s > 4

If s is the longest side, then we require ...

8 +12 > s ⇒ s < 20

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Some authors write the inequality as ...

a +b ≥ c

This allows a "triangle" that looks like a line segment. It will have an area of 0. If your curriculum uses this version of the triangle inequality, then the answer to this question will be 4 ≤ s ≤ 20.

User BPratik
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