Isosceles triangle \( A B C \) has a perimeter of 96 centimeters. The base of the triangle is \( \overline{A C} \) and measures 24 centimeters. What is the measure of \( \overline{A B} \) ? 12 cm 36 cm 48 cm 72 cm

To find the measure of \( \overline{A B} \) in isosceles triangle \( A B C \), we know that the perimeter is the sum of all sides. Since the perimeter is 96 cm and the base \( \overline{A C} \) measures 24 cm, we can set up the equation: \[ \text{Perimeter} = \overline{A B} + \overline{A B} + \overline{A C} \] Let \( \overline{A B} = x \). Therefore, \[ 96 = x + x + 24 \] \[ 96 = 2x + 24 \] \[ 96 - 24 = 2x \] \[ 72 = 2x \] \[ x = \frac{72}{2} = 36 \] Thus, the measure of \( \overline{A B} \) is 36 cm.