Answer:
Step-by-step explanation:
Given that the points A and B are two vertices of an equilateral triangle.
Let a be the side of the triangle
We know that the Area of an equilateral triangle with length of side a is
[tex]Area=\frac{\sqrt{3}}{4}a^2[/tex] square units
Perimeter of the triangle = sum of all sides
=a+a+a
∴ Perimeter of the triangle=3a units
Let equate the Area of the equilateral triangle = Perimeter
Substitute the values we get
[tex]\frac{\sqrt{3}}{4}a^2=3a[/tex]
[tex]\frac{a^2}{a}=\frac{3\times 4}{\sqrt{3}}[/tex]
Therefore [tex]a=4\times \sqrt{3}[/tex] units
Substitute the value of a in the perimeter we get
Perimeter=3a
[tex]3a=3(4\times \sqrt{3})[/tex]
[tex]Perimeter=12\sqrt{3}[/tex] units
=12×1.732
=20.784 units
