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ΔABC has side lengths of 4 and 13. What is the range of possible lengths for the third side of ΔABC?

User XXL
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1 Answer

4 votes

Answer:

The third side must be greater than 9 and less than 17.

9 < x < 17

Explanation:

The Triangle Inequality Theorem says that if you know two sides of a triangle, and you subtract them and you add them (get two separate numbers), the third side will be in between those numbers. So if you have 4 and 13 as the two sides.

13 - 4 is 9. The third side has to be bigger than 9.

Then, 13 + 4 is 17. The third side has to be smaller than 17.

9 < x < 17

User Saadeez
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