isosceles triangle abc has a perimeter of 96 centimeters. the base of the triangle is $overline{ac}$ and…

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 $overline{ab}$?\n12 cm\n36 cm\n48 cm\n72 cm

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 $overline{ab}$?\n12 cm\n36 cm\n48 cm\n72 cm

Answer

Explanation:

Step1: Recall isosceles - triangle property

In an isosceles triangle (ABC) with base (AC), (AB = BC). Let (AB=x), then (BC = x) and (AC = 24) cm, and the perimeter (P=AB + BC+AC).

Step2: Set up the perimeter equation

We know that (P = 96) cm. So, (x + x+24=96). Combining like - terms, we get (2x+24 = 96).

Step3: Solve for (x)

Subtract 24 from both sides of the equation: (2x=96 - 24), so (2x=72). Divide both sides by 2: (x=\frac{72}{2}=36) cm.

Answer:

B. 36 cm