Respuesta :
Answer:
The length of the side of an equilateral traingle [tex]s=2\sqrt{2}[/tex] inches
Step-by-step explanation:
Given that the area of an equilateral triangle is given by
[tex]A=3^\frac{1}{2}s^2[/tex]
It can be written as
[tex]a=\frac{\sqrt{3}}{4} s^2[/tex] Square inches (1)
To find the length of the side s os an equilateral triangle
Given that area of an equilateral triangle is [tex]12^\frac{1}{2}[/tex] square inches
It can be written as
[tex]A=12^\frac{1}{2}[/tex]
[tex]A=\sqrt{12}[/tex] square inches
It can be written as
[tex]A=12^\frac{1}{2}[/tex]
[tex]A=\sqrt{12}[/tex] square inches (2)
Now comparing equations (1) and (2) we get
[tex]\frac{\sqrt{3}}{4}s^2=\sqrt{12}[/tex]
[tex]\frac{\sqrt{3}}{4}s^2=\sqrt{4\times 3}[/tex]
Dividing by [tex]\frac{\sqrt{3}}{4}[/tex] on both sides we get
[tex]\frac{\frac{\sqrt{3}}{4}s^2}{\frac{\sqrt{3}}{4}}=\frac{2\sqrt{3}}{\frac{\sqrt{3}}{4}}[/tex]
[tex]\frac{\sqrt{3}}{4}s^2\times\frac{4}{\sqrt{3}}=2\sqrt{3}\times\frac{4}{\sqrt{3}}[/tex]
[tex]s^2=8[/tex]
[tex]s=\sqrt{8}[/tex]
Therefore [tex]s=2\sqrt{2}[/tex] inches
Therefore the length of the side of an equilateral traingle [tex]s=2\sqrt{2}[/tex] inches
