Question

isosceles triangles
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}?
48 cm
12 cm
36 cm
72 cm

Explanation:

Step1: Recall the perimeter formula of a triangle

The perimeter \(P\) of a triangle \(ABC\) is \(P = AB + BC+AC\). In an isosceles triangle \(ABC\) with \(AB = BC\) (since \(AC\) is the base), the formula becomes \(P=2AB + AC\).

Step2: Substitute the known values into the formula

We know that \(P = 96\) cm and \(AC = 24\) cm. Substituting these values into \(P = 2AB+AC\), we get \(96=2AB + 24\).

Step3: Solve for \(AB\)

First, subtract 24 from both sides of the equation: \(96 - 24=2AB+24 - 24\), which simplifies to \(72 = 2AB\). Then divide both sides by 2: \(AB=\frac{72}{2}\).

Answer:

\(36\) cm