The length of the altitude of the equilateral triangle ABC is [tex]\frac{13\sqrt{3} }{2}[/tex].
Equilateral Triangle is defined as the triangle with all the sides equal and all the angles = 60 deg.
Altitude of a Triangle can be defined as the perpendicular drawn from the vertex of a triangle to the opposite side.
According to the question
In the figure given below
In ΔADC
Since ΔADC is a right angle triangle we can apply Pythagoras Theorem.
Let the sides of the equilateral triangle be "a". and "h" be the altitude.
Since the altitude is of equilateral triangle it divides the base i.e. DC=a/2
[tex](AC)^{2} =(AD)^{2}+(DC)^{2}[/tex]
[tex]a^{2} =h^{2}+(\frac{a}{2})^{2}\\ \\ h^{2}=\frac{4a^{2}-a^{2}}{4} \\ \\ h=\sqrt{3} *\frac{1}{2} *a[/tex]
Substituting the value of a=13 we get
Altitude [tex]h=\frac{13\sqrt{3} }{2}[/tex]
Therefore , The length of the altitude of the equilateral ΔABC is [tex]\frac{13\sqrt{3} }{2}[/tex].
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