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Find the ratio of the numerical value of the area, in square units, of an equilateral triangle of side length $1$ units to the numerical value of its perimeter, in units. Express your answer as a common fraction in simplest radical form.

User ShibbyUK
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Answer:


(√(3))/(12)

Explanation:

The formula for the area of an equilateral triangle is:


\large\boxed{A=(√(3))/(4)s^2}

where "s" is the side length.

To calculate the area of an equilateral triangle with side length 1 unit, substitute s = 1 into the formula for area:


A=(√(3))/(4) \cdot 1^2


A=(√(3))/(4) \cdot 1


A=(√(3))/(4) \; \sf square\;units

Therefore, the area of an equilateral triangle with side length 1 unit is:


\boxed{\textsf{Area}=(√(3))/(4) \; \sf square\;units}

The perimeter of a two-dimensional shape is the distance all the way around the outside. Therefore, the perimeter of an equilateral triangle with side length 1 unit is 3 units (since an equilateral triangle has three sides of equal length).


\boxed{\textsf{Perimeter}=3\; \sf units}

Therefore the ratio of the numerical value of the area to the numerical value of its perimeter is:


\textsf{Area : Perimeter}=(√(3))/(4):3

Express the ratio as a fraction:


((√(3))/(4))/(3)=(√(3))/(4)\cdot (1)/(3)=(√(3))/(12)

Therefore, the ratio of the numerical value of the area, in square units, of an equilateral triangle of side length 1 units to the numerical value of its perimeter, in units, expressed as a common fraction in simplest radical form is:


\Large\boxed{(√(3))/(12)}

User DropsOfJupiter
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