The height of the triangle FGH is equal to 51 units.
Triangle FGH is an equilateral triangle, thus we understand that each of its sides is identical.
Every side's length is specified as 34√3 units.
In order to split HF into two equivalent halves, use a perpendicular bisector. This implies,
34√3/2=17√3
By using the Pythagorean theorem, which states that the total of a triangle's two sides matches the square of its hypotenuse, we may determine the height.
a²+b²=c²
Here, a=17√3
b=height &
c=34√3
Therefore, from the above equation, we can say,
b²=c²-a²
⇒b²=(34√3)²-(17√3)²
⇒b²=([tex]34^{2}*3[/tex])-([tex]17^{2} *3[/tex])
⇒b²=3468-867
⇒b²=2601
⇒b=[tex]\sqrt{2601}[/tex]
⇒b=51 units
Hence, it is concluded that the height of the triangle is (c)51 units.
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