Find the range of possible measures of the third side. \[ 28,35 \]

To find the range of possible measures for the third side of a triangle with the other two sides measuring 28 and 35, we can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides must be greater than the length of the third side. We can set up the inequalities as follows: 1. \( x + 28 > 35 \) → \( x > 7 \) 2. \( x + 35 > 28 \) → \( x > -7 \) (This is always true since side lengths must be positive.) 3. \( 28 + 35 > x \) → \( x < 63 \) Combining the valid inequalities, we can deduce: \[ 7 < x < 63 \] So, the range of possible measures for the third side is between 7 and 63 (not inclusive).