In triangle ABC, AB measures 25 cm and AC measures 35 cm. The inequality lt slt represents the possible third side length of the triangle, s, in centimeters. The inequality lt plt represents the possible values for the perimeter, p of the triangle, in centimeters.

To find the possible third side length of the triangle, we can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.<br /><br />Let's denote the third side length as s. Then, we have the following inequalities:<br /><br />AB + AC > s<br />AB + s > AC<br />AC + s > AB<br /><br />Substituting the given values of AB and AC, we get:<br /><br />25 + 35 > s<br />25 + s > 35<br />35 + s > 25<br /><br />Simplifying these inequalities, we have:<br /><br />60 > s<br />s > 10<br />s > -10<br /><br />Since the length of a side cannot be negative, we can eliminate the last inequality. Therefore, the possible third side length of the triangle is between 10 cm and 60 cm.<br /><br />To find the possible values for the perimeter of the triangle, we need to consider the sum of the lengths of all three sides. Let's denote the perimeter as p. Then, we have:<br /><br />p = AB + AC + s<br /><br />Substituting the given values of AB and AC, we get:<br /><br />p = 25 + 35 + s<br /><br />Simplifying this expression, we have:<br /><br />p = 60 + s<br /><br />Since the possible third side length of the triangle is between 10 cm and 60 cm, we can substitute these values into the expression for p. Therefore, the possible values for the perimeter of the triangle are between 70 cm and 120 cm.<br /><br />In summary:<br />- The possible third side length of the triangle is between 10 cm and 60 cm.<br />- The possible values for the perimeter of the triangle are between 70 cm and 120 cm.