Perimeter of a triangle

🏆Practice perimeter of the triangle

Perimeter: calculating the perimeter of a triangle

To calculate the perimeter of a triangle, all you have to do is add its three sides. If you have all the necessary information, you can solve such a problem in a matter of seconds, for example:

Formula for the perimeter of a triangle:

P = Side 1 + Side 2 + Side 3.

A - The formula of the perimeter of a triangle

If you give us a triangle whose sides have the following measurements:

AB=5 AB = 5

BC=8 BC = 8

CA=6 CA = 6

In this case, the perimeter of the triangle, which is the sum of the 3 3 sides will be equal to. 19 19

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Then, if we are given a triangle whose sides have the following measures:

AB=2 AB = 2

BC=4 BC = 4

CA=6 CA = 6

Its perimeter will be equal to 12 12

Finally, if we are given a triangle whose sides have the following measures:

AB=5 AB = 5

BC=5 BC = 5

CA=5 CA = 5

Its perimeter will be equal to 15 15


"So what's the problem when it comes to calculating the perimeter of a triangle?"

Good question! Many of the problems to calculate the perimeter of a triangle provide us with all the necessary information to calculate the perimeter. However, it is very likely that to solve a problem of this type we also have to previously find the measures of the sides, that is, before calculating the perimeter of the triangle, we will have to perform other operations to obtain all the information we need.

So, regardless of the type of exercise, the steps to follow to find the perimeter of a triangle are the following:

  • Find the value of the sides whose information we do not know.
  • Add all the sides to find the perimeter.

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Example 1

We are given an equilateral triangle of which one side measures 4 4 and are asked to find out what its perimeter is.

Answer:

It is clear that in the case of an equilateral triangle all its sides are equal, so, in this case its perimeter will equal P=4+4+4=12 P=4+4+4=12 .


Example 2

We are given an isosceles triangle whose side A measures 12 12 and whose perimeter equals 30 30 . How long is the base?

Answer: Since in an isosceles triangle opposite sides are equal, side B will also measure 12 12 . So far, the sum of the two opposite sides equals 24 24 . To find out how long the base of the triangle is, we must subtract the value of the sum of the sum of the opposite sides from the total value of the perimeter, that is:

3024=6 30 - 24 = 6 .

Thus, the base will be equal to 6 6 .


Do you know what the answer is?

Example 3

We are given an equilateral triangle whose perimeter equals 90 90 . How long are its sides?

Answer:

Since in an equilateral triangle, all sides measure the same. The perimeter of 90 90 is divided by the three equal sides, so each side will measure 30 30 .


Example 4

We are given an isosceles triangle whose perimeter equals 37 37 and whose side B measures 10 10 . How long is the base?

Answer:

Since in an isosceles triangle the opposite sides are equal, side A will also measure 10 10 . To find out how long the base of the triangle is, we must subtract the value of the sum of the sum of the opposite sides from the total value of the perimeter, that is:

3720=7 37 - 20 = 7

Thus, the length of the base is 7 7 .


Check your understanding

Silly mistakes when calculating the perimeter

Finding the perimeter of a triangle is very simple and all it requires is that you master the addition operation. In some problems you will have all the necessary information about the sides of the triangle, but in other cases you will have to find the information you need by yourself, taking into account the characteristics of each type of triangle: right triangle, isosceles, equilateral or scalene.

Therefore, it is important that you know the characteristics that distinguish each type of triangle. The best way to memorize them is by means of a table containing the following information:

  • Name of the triangle
  • Specific characteristics of the triangle
  • An example of this type of triangle

How to practice with problems of calculating the perimeter of a triangle?

The key to mastering this topic is to practice with many exercises, the more problems the better and the more types the better. As we have already said, not all the problems will provide you with all the information, but you will have to find it with the data you have been given. It is important to remember that many times we focus only on the easy exercises that are marked as homework, but it is better if we get out of our comfort zone and practice with exercises that are a little more difficult. We have a proposal for you: To review the characteristics of each type of triangle, practice with several problems for each type; this way you will better understand their characteristics. For example: do ten exercises on isosceles triangles, another ten on equilateral triangles, and so on. Then mix different types of problems: some in which you are given the perimeter and asked what is the length of each side; some in which you are given the value of a side and must find the perimeter, and so on.


Do you think you will be able to solve it?

Triangle Perimeter Calculation Exercises

Exercise 1 (Perimeter of an equilateral triangle )

Given the equilateral triangle

Exercise 1 Given the equilateral triangle

Homework:

What is its perimeter?

Solution:

In an equilateral triangle all its sides are equal, therefore its perimeter is equal to the sum of its sides. All it entails is to add the data together.

5+5+5=15 5 + 5 + 5 = 15

Answer:

The perimeter of the triangle is equal to. 15 15


Exercise 2 (Perimeter of an isosceles triangle)

Given the isosceles triangle:

Exercise 2 Given the isosceles triangle

The perimeter of the triangle is equal to 50 50 .

Task:

What is the value of X X ?

Solution:

In the isosceles triangle, there are two equal sides. According to the figure we can observe that the remaining side is also equal to X X , so it is equal to the second side.

We know that the perimeter of the triangle is equal to the sum of its three sides.

Now, we replace in the formula:

X+X+5.6=50 X + X + 5.6 = 50

2X+5.6=50 2X + 5.6 = 50

We subtract the 5.6 5.6

2X=44.4 2X = 44.4

Divide by two

X=22.1 X = 22.1

Answer:

And we find that X=22.1 X = 22.1


Test your knowledge

Exercise 3

Given the right triangle ADB

Given the right triangle ADB \triangle ADB

The perimeter of the triangle is equal to 30cm 30\operatorname{cm} .

Given: AB=15,AC=13,DC=5,CB=4 AB = 15, AC = 13, DC = 5, CB = 4

Task:

Calculate the area of the triangle. ABC \triangle ABC

Solution:

Given the perimeter of the triangle ADC \triangle ADC equal to 30cm 30\operatorname{cm} .

From here we can calculate AD AD .

AD+5+13=30 AD + 5 + 13 = 30

AD+18=30 AD + 18 = 30

AD=12 AD = 12

Now we can calculate the area of the triangle ΔABC ΔABC

Pay attention: we are talking about an obtuse triangle so its height is AD AD

We use the formula to calculate the area of the triangle:

A=altura×base2A = \frac{altura\times base}{2}

A=AD×BC2=12×42=482=24A = \frac{AD \times BC}{2} = \frac{12 \times 4}{2} = \frac{48}{2} = 24

Answer:

The area of the triangle ΔABC ΔABC is equal to 24cm2 24cm² .


Exercise 4

Given the triangle and the circumference in the figure, which has the larger perimeter?

Exercise 4 Given the triangle and the circle

Task:

Which figure has the largest perimeter?

Solution:

In the beginning we will start with the triangle:

P=AB+BC+CA P = AB + BC + CA

=AB+BC+CD+DA = AB + BC + CD + DA

Using Pythagoras:

CD2=BC2BD2=5242=9 CD² = BC² - BD² = 5² - 4² = 9

We obtain its root

CD=3cm CD = 3 \operatorname{cm}

Again we use Pythagoras:

AD2=AB2BD2=6242=20 AD² = AB² - BD² = 6² - 4² = 20

We obtain its root

AD=4.47cm AD = 4.47 \operatorname{cm}

With the information obtained we calculate its perimeter.

P=6+5+3+4.47 P = 6 + 5 + 3 + 4.47

=18.47 = 18.47

Now we move on to the circle:

P=2πR P = 2πR

=2π×6 = 2π \times 6

=12π = 12π

=12×3.14 = 12 \times 3.14

=37.68 = 37.68

Answer:

The perimeter of the circle is larger.


Do you know what the answer is?

Exercise 5

Given the triangle in the figure:

Exercise 5 - Given the triangle of the figure

Homework:

What is its perimeter?

Solution:

Using Pythagoras

AB2+BC2=AC2 AB² + BC² = AC²

49+9=AC2 49 + 9 = AC²

58=AC2 58 = AC²

We obtain its root

58=AC \sqrt{58} = AC

We obtain the perimeter

P=AB+BC+AC P = AB + BC + AC

P=7+3+58=10+58 P = 7 + 3 + \sqrt{58} = 10 + \sqrt{58}

Answer:

P=10+58 P = 10 + \sqrt{58}


Questions and answers on the subject:

What is the perimeter of a triangle?

It is the length of the outline of the triangle.


What is the formula for calculating the perimeter of a triangle?

Given a triangle ΔABC ΔABC , the formula is P=AB+BC+CA P=AB+BC+CA


In which case can the perimeter of a triangle be calculated knowing only one of its sides?

In the case where the triangle is equilateral, since all sides are equal and the perimeter would be the result of adding three times the known side.


Check your understanding

"I don't get to solve all the problems on the exam. What do I do?"

This is really frustrating: they take points off the exam for not knowing how to manage time, not because you don't know the lesson. It is advisable that you "research" the exam and find out if it is just something specific or, on the contrary, something more general. Talk it over with your teacher to find out what the reason is:

  • nerves caused you to draw a blank
  • you did not know all the content of the lesson
  • you need more time

Why is it worthwhile to solve perimeter problems?

Problems where you have to find the perimeter of a triangle are essential! Why? Adding the sides requires nothing more than knowing how to add. However, the more problems you solve, the more you will learn about triangles and the characteristics of each triangle. We recommend that you practice problems of this type with as many types of triangles as possible. In this way you will learn everything there is to know about triangles in a comprehensive way.


Do you think you will be able to solve it?

Calculating the perimeter: a relevant question for all courses

No matter what course you go to, finding the perimeter of a triangle is one of the most recurring topics in all groups, albeit with varying levels of difficulty.


If you are interested in learning more about other triangle topics, you can enter one of the following articles:

On the Tutorela blog you will find a variety of articles about mathematics.


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examples with solutions for perimeter of the triangle

Exercise #1

Given the triangle:

777111111131313

What is its perimeter?

Video Solution

Step-by-Step Solution

The perimeter of a triangle is equal to the sum of all its sides together:

11+7+13=11+20=31 11+7+13=11+20=31

Answer

31

Exercise #2

Look at the triangle below:

666888101010

What is the perimeter of the triangle?

Video Solution

Step-by-Step Solution

The perimeter of the triangle is equal to the sum of all sides together, therefore:

6+8+10=14+10=24 6+8+10=14+10=24

Answer

24

Exercise #3

Given an equilateral triangle:

555

What is its perimeter?

Video Solution

Step-by-Step Solution

Since the triangle is equilateral, that is, all sides are equal to each other.

The perimeter of the triangle is equal to the sum of all sides together, the perimeter of the triangle in the drawing is equal to:

5+5+5=15 5+5+5=15

Answer

15

Exercise #4

Given the isosceles triangle,

777121212

What is its perimeter?

Video Solution

Step-by-Step Solution

Since the triangle is isosceles, that means its two legs are equal to each other.

Therefore, the base is 7 and the other two sides are 12.

The perimeter of a triangle is equal to the sum of all sides together:

12+12+7=24+7=31 12+12+7=24+7=31

Answer

31

Exercise #5

Look at the isosceles triangle below:

444666

What is its perimeter?

Video Solution

Step-by-Step Solution

Since we are referring to an isosceles triangle, the two legs are equal to each other.

In the drawing, they give us the base which is equal to 4 and one side is equal to 6, therefore the other side is also equal to 6.

The perimeter of the triangle is equal to the sum of the sides and therefore:

6+6+4=12+4=16 6+6+4=12+4=16

Answer

16

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