Question

isosceles triangle abc has a perimeter of 96 centimeters. the base of the triangle is \\(\overline{ac}\\) and measures 24 centimeters. what is the measure of \\(\overline{ab}\\)? \\(\bigcirc\\) 12 cm \\(\bigcirc\\) 36 cm \\(\bigcirc\\) 48 cm \\(\bigcirc\\) 72 cm

Explanation:

Step1: Recall isosceles triangle properties

In an isosceles triangle, the two equal sides (legs) are equal. Here, base is \( \overline{AC} = 24 \) cm, and let the length of \( \overline{AB} \) (a leg) be \( x \). Then the other leg \( \overline{BC} \) is also \( x \).

Step2: Use perimeter formula

Perimeter \( P = AB + BC + AC \). Given \( P = 96 \) cm, \( AC = 24 \) cm, so \( 96 = x + x + 24 \).

Step3: Solve for \( x \)

Simplify the equation: \( 96 = 2x + 24 \). Subtract 24 from both sides: \( 2x = 96 - 24 = 72 \). Then divide by 2: \( x = \frac{72}{2} = 36 \).

Answer:

36 cm (corresponding to the option "36 cm")