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An equilateral triangle's perimeter and side lengths vary ____ with one another.

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Detailed Solution

An equilateral triangle's perimeter and side lengths vary directly with one another.
We have given an equilateral triangle.
We know that if two quantities

x

and

y

vary in the same way while maintaining a constant ratio between their respective values, then the two quantities are said to be in direct proportion.
i.e.

x y = k,

where k is a constant positive number.
The perimeter of an equilateral triangle is given by

Perimeter = 3 a ⇒ Perimeter a = 3

Where the side of the equilateral triangle is

a

unit.
As a result, the equilateral triangle's perimeter is directly proportional to the length of each of its sides.

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