To determine the height of the triangular base of a pyramid with an equilateral triangle as its base, you follow these steps:
1. Identify the given value: The edge length of the equilateral triangle, denoted as [tex]\( s \)[/tex], is given as 5 units.
2. Recall the formula for the height of an equilateral triangle: This formula is derived from the properties of equilateral triangles. For any equilateral triangle with side length [tex]\( s \)[/tex], the height ([tex]\( h \)[/tex]) can be found using the formula:
[tex]\[
h = \frac{\sqrt{3}}{2} \cdot s
\][/tex]
3. Plug in the given value of [tex]\( s \)[/tex] into the formula: Given that [tex]\( s = 5 \)[/tex] units, substitute 5 into the formula:
[tex]\[
h = \frac{\sqrt{3}}{2} \cdot 5
\][/tex]
4. Simplify the expression: Perform the multiplication to acquire the final expression:
[tex]\[
h = \frac{5\sqrt{3}}{2}
\][/tex]
This is the height of the equilateral triangular base of the pyramid. Therefore, the correct expression representing the height is:
[tex]\[
\frac{5}{2} \sqrt{3} \text{ units}
\][/tex]
Hence, the correct option is:
[tex]\[
\frac{5}{2} \sqrt{3} \text{ units}
\][/tex]
