State if the three numbers can be the measures of the sides of a triangle. 6, 9, 10

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No. They cannot be the measures of the sides of a triangle.

Step-by-step explanation:

Using Pythagorean Theorem (a² + b² = c²) we can find out if these measures match.

The order for a and b doesn't matter, but the measure for c does. c is the hypotenuse, the longest side of a triangle. With these measures, 10 will be the hypotenuse because it is the longest.

6² + 9² = 10²  If this is true, then the measures can be sides of a triangle.

117 = 100   6 squared plus 9 squared equals 117 but 10 squared equals 100. They do not match so the answer is no.