The expression that represents the height of the triangular base of the pyramid is given by: Option B: (5/2)√3 untis
If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
The question is incomplete, and the upper part of the completed question is:
"The base of a solid oblique pyramid is an equilateral triangle with an edge length of 5 units. A solid oblique pyramid has an equilateral triangle base with an edge length of 5 units. "
The diagram of the base of the considered pyramid is attached below.
The perpendicular from A to BC is touching BC at C, and is bisecting it (it can be proved).
Consider the triangle ADB. It is a right angled triangle.
We need the length of AD which represents the height of the triangle ABC.
This is obtained using Pythagoras theorem as:
[tex]|AB|^2 = |AD|^2 + |DB|^2\\\\|AD|^2 = |AB|^2 - |DB|^2\\\\|AD| = \sqrt{5^2 - \left( \dfrac{5}{2}\right)^2}[/tex]
(took positive root because of |AD| being length, which is a non-negative quantity).
SImplifying it, we get:
[tex]|AD| = \sqrt{5^2 - \left( \dfrac{5}{2}\right)^2}\\\\|AD| = \sqrt{\dfrac{5^2(4-1)}{4}} = \dfrac{5\sqrt{3}}{2} = \dfrac{5}{2} \times \sqrt{3} \: \rm units[/tex]
Thus, the expression that represents the height of the triangular base of the pyramid is given by: Option B: (5/2)√3 untis
Learn more about Pythagoras theorem here:
https://brainly.com/question/12105522
