Concept:Understanding the properties of an equilateral triangle and using the relationship between its perimeter, side length, and altitude.Formulas Used:Perimeter of an equilateral triangle = $3 \times side$Altitude of an equilateral triangle = $\frac{\sqrt{3}}{2} \times side$Explanation:We are given that the perimeter of an equilateral triangle is 24 cm.Let the side length of the equilateral triangle be $a$.The perimeter is given by $3a$.So, $3a = 24$ cm.Dividing by 3, we get the side length $a = \frac{24}{3} = 8$ cm.Now, we need to find the altitude (height) of the equilateral triangle.The formula for the altitude of an equilateral triangle is $h = \frac{\sqrt{3}}{2} \times a$.Substituting the value of $a = 8$ cm into the formula:$h = \frac{\sqrt{3}}{2} \times 8$$h = 4\sqrt{3}$ cm.Answer:The altitude of the equilateral triangle is $4\sqrt{3}$ cm.The correct option is D.