What is the ratio of the area of an equilateral triangle, in square inches, to its perimeter, in inches?

If the side of the triangle is ' S ', then . . .
-- Base of the triangle = S -- Height of the triangle = 1/2 S √3
-- Area = 1/2 (base) (height) = (S² √3) / 4
-- Perimeter = 3 S
Area / Perimeter (numerical) = [ (S² √3) / 4 ] / 3 S
That ugly thing becomes ***S √3 / 12 *** .

Answered by AL2006 | 2024-06-10

The ratio of the area of an equilateral triangle to its perimeter can be calculated by considering the properties of the triangle. An equilateral triangle has all three sides equal in length, so the perimeter is equal to 3 times the length of one side. The formula for the area of an equilateral triangle is √3/4 × (side length)².
To find the ratio, we can set up the following proportion:

Ratio of area to perimeter = (Area of triangle) / (Perimeter of triangle)
Ratio of area to perimeter = (√3/4 × (side length)²) / (3 × side length)

Cancel out the common factor of side length and simplify:

Ratio of area to perimeter = (√3/4 × (side length)) / 3
Ratio of area to perimeter = √3/12

The ratio of the area of an equilateral triangle to its perimeter is √3/12.

Answered by RachelMeghanMarkle | 2024-06-18

The ratio of the area of an equilateral triangle to its perimeter is given by 12 S 3 ​ ​ , where S is the side length of the triangle. This formula demonstrates the relationship between a triangle's area and perimeter based on its dimensions. Understanding this ratio helps in various geometric applications.
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Answered by AL2006 | 2024-09-26