Content

• To step
• Method 1 of 3: Calculate the perimeter of a triangle when the lengths of all sides are given
• Method 2 of 3: Calculate the circumference if only two sides of the triangle are given
• Method 3 of 3: Finding the perimeter of a triangle with the law of cosines

The perimeter of a triangle is the length of a line that you can draw along the sides of the triangle. The easiest way is to add the lengths of all sides together, but if you don't know all the lengths, you have to calculate them first. This article will first teach you how to calculate the circumference of a triangle if you know the lengths of all three sides; this is the easiest and most used method. Then you will learn how to calculate the circumference if you only know the lengths of two of the three sides. Finally, it explains how to calculate the perimeter if you know the lengths of two sides and the angle between them, using the law of cosines.

To step

Method 1 of 3: Calculate the perimeter of a triangle when the lengths of all sides are given

1. Learn the formula for finding the circumference. The formula is: A + B + C = X at which a, B., and C. represent the lengths of the sides and X the outline.
   • This formula basically means that to find the perimeter of a triangle, you have to add the lengths of the three sides together.
2. Determine the lengths of all three sides. In this example: a = 5, B. = 5, C. = 5.
   • You are now working on an equilateral triangle because all three sides of the figure are exactly the same length. But keep in mind that this formula applies to all triangles.
3. Add the lengths of the three sides together. In this example: 5 + 5 + 5 = 15. So the perimeter of the triangle (X) is 15.
   • Another example: If a = 4, b = 3, and c = 5, then the circumference is 3 + 4 + 5, in other words 12.
4. Remember to always include the units with your answer. If the sides are in centimeters, your final answer should also be in centimeters. If the sides are given in terms of a variable, for example x, then the answer must also be in terms of x.
   • In this example, the sides are all 5 cm, so the correct answer is 15 cm.

Method 2 of 3: Calculate the circumference if only two sides of the triangle are given

1. Know what a right triangle is. A right triangle is a triangle with a right angle (90 degrees). The side of the triangle opposite that right angle is always the longest side, which is called the hypotenuse or the hypotenuse. Right triangles pop up regularly in math tests, but luckily there is a very handy formula for calculating the length of unknown side!
2. Know the Pythagorean theorem. The Pythagorean theorem applies to any right triangle, and reads: a² + b² = c².
3. Look at your triangle and write on the sides a, b and c. Remember that the longest side is called the hypotenuse. This one is opposite the right angle, and you have to reach this side c to write. You write on the two shorter sides a and b. It doesn't matter which one you put where, the outcome will be the same!
4. Copy the lengths of the sides into the Pythagorean theorem. Remember that a + b = c. Enter the lengths in the place of the corresponding letters.
   • For example, if you know silk a = 3 and silk b = 4, you write it like this in the formula: 3 + 4 = c.
   • A second example: When you know the length of side a = 6, and the hypotenuse c = 10, then put it in the equation like this: 6 + b = 10.
5. Solve the equation to find the missing length. You must first multiply the known sides by themselves (for example 3 = 3 * 3 = 9). If you're looking for the hypotenuse, you can then just add the two values ​​together and calculate the square root of the result to find the length. If you miss another side, subtract the two and then calculate the square root of the result to find the length.
   • In the first example, you multiply the values ​​in 3 + 4 = c and you discover that and 25 = c. Then calculate the square root of 25 so that you arrive at c = 25.
   • In the second example, you multiply the values ​​in 6 + b = 10 and you find out 36 + b = 100. Subtract 36 from 100 to get to b = 64, and then calculate the square root of 64 to get b = 8.
6. Add the lengths of the three sides to calculate the circumference. Remember the equation: X = a + b + c. Now you have the lengths of the sides a, b and c you can add them together to get the circumference.
   • In the first example that is X = 3 + 4 + 5, or 12.
   • In the second example that is X = 6 + 8 + 10, or 24.

Method 3 of 3: Finding the perimeter of a triangle with the law of cosines

1. Learn the law of cosines. With the law of cosines, you can solve any triangle if you know the lengths of two sides and the angle between them. It works with any triangle, and it's a really useful formula. The law of cosines states that, for every triangle with sides a, b, and c, with opposite corners a, B., and C. the following formula applies: c = a + b - 2ab cos(C).
2. Look at your triangle and put the letters next to the different parts. You must be the first side you know a call, and the opposite corner is then a. You have to know the second side you know b call it, the opposite corner B.. You have to know the angle you know C. and the third side, the one you want to solve, is then c.
   • For example, imagine a triangle with a side of 10 and one of 12, and an angle of 97 ° in between. We then write the variables as follows: a = 10, b = 12, C = 97 °.
3. Put your information in the equation and solve side c. First you have to multiply a and b by themselves and add them together. Then calculate the cosine of C with the cosfunction on your calculator, or an online calculator. Multiply cos(C) with 2ab and subtract the result from the sum of a + b. The answer is c. Calculate the square root of this and you know the length of the side cIn our example:
   • c = 10 + 12 - 2 × 10 × 12 × cos(97).
   • c = 100 + 144 - (240 × -0.12187) (Round the cosine to 5 decimal places)
   • c = 244 - (-29.25)
   • c = 244 + 29.25 (Include the minus sign as cos(C) is negative!)
   • c = 273.25
   • c = 16.53
4. Use the length of c to calculate the circumference of your triangle. Remember that the formula for the circumference is: X = a + b + c, so you just have to add all the lengths together, because a and b you already knew. Piece of cake!
   • In our example: 10 + 12 + 16,53 = 38,53, that's the circumference of our triangle!