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The base of a solid oblique pyramid is an equilateral triangle with an edge length of 5 units.

Which expression represents the height of the triangular base of the pyramid?

A. [tex]\(\frac{s}{2} \sqrt{2}\)[/tex] units
B. [tex]\(\frac{5}{2} \sqrt{3}\)[/tex] units
C. [tex]\(s \sqrt{2}\)[/tex] units
D. [tex]\(5 \sqrt{3}\)[/tex] units

Sagot :

To determine the height of the triangular base of the pyramid, we start by recalling that the base is an equilateral triangle with an edge length of [tex]\(5\)[/tex] units.

For an equilateral triangle with side length [tex]\(s\)[/tex], the height can be calculated using the formula:
[tex]\[ \text{Height} = \frac{s \sqrt{3}}{2} \][/tex]

Given that the side length [tex]\(s = 5\)[/tex] units, we substitute [tex]\(s\)[/tex] into the formula:
[tex]\[ \text{Height} = \frac{5 \sqrt{3}}{2} \][/tex]

Thus, the height of the triangular base of the pyramid is:
[tex]\[ \frac{5}{2} \sqrt{3} \][/tex]

Therefore, the correct expression that represents the height of the triangular base of the pyramid is:
[tex]\[ \frac{5}{2} \sqrt{3} \text{ units} \][/tex]
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