The height is 51 units.
Step-by-step explanation:
Given that triangle FGH is a equilateral triangle then you know all its sides are equal.
The length of each side is given as 34√3 units.
A perpendicular bisector will divide HF into two equal parts. This means;
[tex]34\sqrt{3} /2 =17\sqrt{3}[/tex]
Find the height by applying the pythagorean relationship where sum of the two sides of the triangle equals the square of the hypotenuse.
a²+b²=c² where a=17√3 , b=height and c=34√3
b²=c²-a²
b²= (34√3)²-(17√3)²
b²=(34²*3)-(17²*3)
b²=3468-867
b²=2601
b=√2601
b=51 units
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Pythagorean relationship:https://brainly.com/question/10812175
Keywords : triangle, equilateral, sides, perpendicular bisector, height
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