Answer:
The length of each side of the equilateral triangle is 6.93 cm.
Step-by-step explanation:
Check the image uploaded for diagram;
The length of each side of the equilateral triangle is y;
Apply Pythagoras theorem to determine y;
[tex]y^2 = 6^2 \ + \ (\frac{y}{2} )^2\\\\y^2 = 36 \ + \ \frac{y^2}{4} \\\\multiply\ through \ by \ 4;\\\\4y^2 =144 \ + \ y^2\\\\4y^2 - y^2 = 144\\\\3y^2 = 144\\\\y^2 = \frac{144}{3} \\\\y^2 = 48\\\\y = \sqrt{48} \\\\y = 6.93\ cm[/tex]
Therefore, the length of each side of the equilateral triangle is 6.93 cm.
A equilateral triangle is the triangle in which all the three sides are of equal length in measure.
The side of the equilateral triangle is 4 centimetres. Hence the option A is the correct option.
A equilateral triangle is the triangle in which all the three sides are of equal length in measure.
The relation between the height and the side of the equilateral triangle can be given as,
[tex]a=\dfrac{2h}{\sqrt{3} }[/tex]
Given information-
An equilateral triangle has a height of 6 centimetres.
The side of the equilateral triangle which has a height of 6 centimetres can be calculate using the above formula. Thus,
[tex]a=\dfrac{2\times6}{\sqrt{3} }\\a=\dfrac{12}{3} \\a=4[/tex]
Thus the side of the equilateral triangle is 4 centimetres. Hence the option A is the correct option.
Learn more about the equilateral triangle here;
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