Question

The perimeter of an equilateral triangle is 1/8 unit. What is the length, in units, of each side of the triangle

Answer 1

The length of each side of an equilateral triangle with a perimeter of 1/8 unit is 1/24 unit.

Step-by-step explanation:

The question involves determining the length of each side of an equilateral triangle if the perimeter of the triangle is 1/8 unit. In an equilateral triangle, all three sides are equal in length. Since the perimeter is the total length around the triangle, and the perimeter given is 1/8 unit, we divide this perimeter by 3 (the number of sides) to find the length of each side.

To calculate:
Perimeter of equilateral triangle = sum of all three sides = 3 × (length of one side)
Therefore, length of one side = Perimeter ÷ 3

Now, substituting the given perimeter:
Length of one side = (1/8 unit) ÷ 3 = 1/24 unit

Answer 2

`{\longrightarrow \pmb{\sf {\qquad (1)/(24) }}} \\ \\`

`\:`

Step-by-step explanation:

It is given that the perimeter of an equilateral triangle is 1/8 unit and we have to find the length of each side of the triangle.

So, we know that,

`\\ {\longrightarrow \pmb{\sf {\qquad 3a = Perimeter_((Equilateral triangle) )}}} \\ \\`

Now, substituting the given values in the formula :

`\\ {\longrightarrow \pmb{\sf {\qquad 3a = (1)/(8) }}} \\ \\`

By doing cross multiplication we get :

`{\longrightarrow \pmb{\sf {\qquad 3a(8) = 1(1) }}} \\ \\`

`{\longrightarrow \pmb{\sf {\qquad 24a = 1 }}} \\ \\`

Dividing both sides by 24 we get :

`\\ {\longrightarrow \pmb{\sf {\qquad (24a)/(24) = (1)/(24) }}} \\ \\`

`{\longrightarrow \pmb{\sf {\qquad a = (1)/(24) }}} \\ \\`

Therefore,

• The length of each side of the triangle is 1/24 units