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} \\)? 12 cm 36 cm 48 cm 72 cm

Explanation:

Step1: Recall the perimeter formula for a triangle

The perimeter \( P\) of a triangle \(ABC\) is \(P = AB + BC+AC\). Since \(ABC\) is isosceles with base \(AC\), \(AB = BC\). Let \(AB=x\), then \(BC = x\) and \(AC = 24\), \(P=96\).

Step2: Substitute into the perimeter formula

Substitute into \(P = AB + BC + AC\), we get \(96=x + x+24\). Simplify the equation: \(96 = 2x+24\).

Step3: Solve for \(x\)

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

Answer:

\(36\mathrm{cm}\)