Question

Two sides of a triangle have the following measures. Find the range for the measure of the third side.

Answer 1

The possible values for the third side's measurement are3 < x < 17. Any two sides of a triangle's lengths added together must be longer than the third side.

How do you determine a triangle's perimeter?

• The third side of a triangle must always have a length that is between (but not exactly) the sum and the difference of the other two sides.
• Any two sides of a triangle's lengths added together must be longer than the third side.
• Each side of a triangle with sides a, b, and c must fall within the difference and total of the other two.
• For instance, side a must be between b-c and b+c or b-cab+c.  
• The third side must fall between 10 -7 = 3 and 10 + 7 = 17.    

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