Question

if an equilateral triangle has a perimeter of 2 2/5 ft what is the length of each side of the triangle ?

Answer 1

General category: Mathematics

Sub-category: Improper fractions

Topic: Mixed number

Introduction:

A mixed number is a whole number plus a fractional part. On the other hand, an improper fraction is a fraction where the numerator is larger than the denominator.

Step-by-step explanation:

We have an equilateral triangle that has a perimeter of

`2(2)/(5)\text{ ft}`

Notice that this number is a mixed number. To convert this mixed number to an improper fraction, we can perform the following steps:

Step 1: multiply the denominator by the whole number

`\text{ 5 x 2 = 10}`

Step 2: add the answer from Step 1 to the numerator

`\frac{10\text{ +2 }}{5}\text{ }`

Step 3: write the answer from Step 2 over the denominator

`\frac{1\text{2 }}{5}\text{ }`

now, if the given triangle is an equilateral triangle, this means that the measure of each of its sides is the same. By definition, the perimeter of a polygon is the sum of its sides, thus if we denote by s any side of the equilateral triangle, we get the following equation:

`\frac{1\text{2 }}{5}\text{ = s+s+s= 3s}`

or

`\frac{1\text{2 }}{5}\text{ = 3s}`

solving for s, we obtain:

`s\text{ = }(12)/(15)=(4)/(5)`

We can conclude that the correct answer is:

Answer:

The length of each side of the equilateral triangle is:

`(4)/(5)`