Perimeter of a Triangle with Fractions Calculator

Created by Davide Borchia
Reviewed by Anna Szczepanek, PhD
Last updated: Oct 11, 2022

Find the perimeter of any triangle with sides described by fractions with our perimeter of a triangle with fractions calculator.

Calculating the perimeter of a triangle is not a big deal, but would you mind some help when the length of the sides starts becoming a fraction?

In this article, we will teach you how to find the perimeter of a triangle with fractions as values of the sides.

How to find the perimeter of a triangle

The perimeter of a triangle is nothing but the sum of its sides.

The three sides of a trinangle
A triangle is commonly defined by its three sides: each combination of three values creates a single and unique triangle (this is not true for quadrilaterals, for example).

It is as easy as it sounds:

P=a+b+cP = a+b+c

How to find the perimeter of a triangle with fractions

You may find a problem where the values of the sides of the triangle are not integer numbers, but either a fractions (like ab\tfrac{a}{b}), or mixed numbers (like abca\tfrac{b}{c}). Worry not: we will teach you how to calculate the perimeter in those situations!

Follow these steps:

  1. Find the values of the sides.
  2. If the denominators of the three fractions are different, find the common denominator (the least common multiple of the trio).
  3. For each fraction, find the new numerator dividing the common denominator by the original denominator and then multiplying the result by the original numerator.
    • If one or more numbers are mixed numbers, simply multiply the **number of wholes by the denominator and then sum the result to the value of the numerator of the proper fraction.
  4. Sum the new numerators.
  5. If possible, simplify the result. If the fraction is improper (the numerator is bigger than the denominator), extract as many integers as you can and write the result as a mixed number.

You are all set!

How to use our perimeter of a triangle with fractions calculator

Insert the known values in the three fields for the sides of the triangle. You can insert the number in the proper and improper fraction format. Separate numerator and denominator with a symbol //.

🙋 Remember that you can insert mixed numbers in our calculator. Simply write them in the form a+b/ca + b/c.

Let's see an example calculation. Imagine you have a triangle with sides:

  • First side a=215a = 2\tfrac{1}{5};
  • Second side b=47b=\tfrac{4}{7}; and
  • Third side c=158c = \tfrac{15}{8}.

To convert the value of the side aa from mixed number to improper fraction, use our mixed number to improper fraction calculator, or follow these simple steps:

215=105+15=1152\frac{1}{5}= \frac{10}{5}+\frac{1}{5} = \frac{11}{5}

Now let's set up the perimeter sum:

P=115+47+158P = \frac{11}{5}+\frac{4}{7}+\frac{15}{8}

We find the common denominator: using the prime factorization method we find that the highest powers of the prime factors are:

71, 51, 237^1,\ 5^1,\ 2^3

Which means that the least common multiple is:

578=2805\cdot7\cdot8=280

Let's move on with the sum. For each side, we find the new numerators:

  • aa: 112805=61611\cdot\tfrac{280}{5}=616;

*bb: 42807=1604\cdot\tfrac{280}{7} =160; and

  • cc: 152808=52515\cdot\tfrac{280}{8}=525.

Now we can calculate the sum:

P=616280+160280+525280=616+160+525280=1301280=4181280\begin{align*} P& = \frac{616}{280}+\frac{160}{280}+\frac{525}{280}\\ \\ & = \frac{616+160+525}{280} = \frac{1301}{280}\\ \\ &=4\frac{181}{280} \end{align*}

The result is not that pretty, but the Math checks out!

More ways to find the perimeter of a triangle

Triangles are an endless source of mathematical surprises. Find more ways to calculate the perimeter of a triangle with our series of calculators:

FAQ

How do I find the perimeter of a triangle with fractions?

To find the perimeter of a triangle with fractions you need to perform a fraction sum. Follow these steps:

  1. Identify the common denominator of the three fractions.
  2. Multiply the numerator of each fraction by the ratio between the common denominator and the respective denominator.
  3. Sum the new numerators.
  4. Eventually simplify the result.

What is the perimeter of a triangle with sides a = 1/2, b = 1/3, and c = 1/4?

P = 13/12. To find the perimeter of a triangle with sides a = 1/2, b = 1/3, and c = 1/4, follow these steps:

  1. Find the common denominator. In this case:
    3 × 2² = 12
  2. Multiply the numerator of each fraction by the ratio between the common denominator and the denominator:
    a = 1 × (12/2)/12 = 6/12
    b = 1 × (12/3)/12 = 4/12
    c = 1 × (12/4)/12 = 3/12
  3. Sum the numerators:
    a + b + c = (6 + 4 + 3)/12 = 13/12

What is the formula for the perimeter of a triangle in fractions?

The formula for the perimeter of a triangle with fractions is the same as the formula for the perimeter of a triangle with any kind of number:
P = a + b + c.

The only difference lies in the way we sum the sides: in this case you have to sum three fractions.

What is the perimeter of a triangle with mixed numbers?

If the sides of a triangle are expressed with mixed numbers you can still apply the rules used in finding the perimeter of a triangle with fractions.

The wholes in front of the fractions can be summed independently from the fractions themselves. Sum the fractions, and add the result to the wholes, or keep it in mixed number format.

Davide Borchia
perimeter of a triangle given 3 sides
a
in
b
in
c
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Perimeter
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