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What is the ratio of the numerical value of the area, in square units, of an equilateral triangle of side length 4 units to the numerical value of its perimeter, in units? Express your answer as a common fraction in simplest radical form.

 Dec 23, 2021
 #1
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It's asking for a ratio between the perimeter and area of an equilateral triangle with sides of 4 units. 

 

So, we need to calculate both perimeter and area. 

 

Perimeter:

4 * 3 = 12 units 

 

Area: 

\(a = {\sqrt{3} x^2 \over{4}}\)

 

\(={4\sqrt3}\)

 

Notice - it's asking for a ratio for Area to Perimeter. So the answer should have area in numerator, and perimeter in denominator. 

\({4\sqrt3\over12} = {\sqrt3\over3}\)

And that's your answer. 

 

In my solution I used the area of an equilateral equation. If you've never seen it before, research it. Google has great sources to clarify it for you. 

 Dec 23, 2021
edited by MathyGoo13  Dec 23, 2021
 #2
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Area of equilateral triangle

 

 Each half of the triangle is   1/2 b * h       b = 2    h = 4 cos 60 =   4 sqrt 3/2  =    2 sqrt 3

    so each is      1/2   2    2 sqrt3 = 2 sqrt 3   

 

There is two of these triangles in the equilateral triangle so total area = 2 * 2 sqrt 3 = 4 sqrt 3   ( as MG 13 found)

 

Guest Dec 23, 2021

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