Perimeter of a triangle

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

$AB = 2$

$BC = 4$

$CA = 6$

Its perimeter will be equal to $12$

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

$AB = 5$

$BC = 5$

$CA = 5$

Its perimeter will be equal to $15$

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.

We are given an equilateral triangle of which one side measures $4$ 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 $P=4+4+4=12$.

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

Answer: Since in an isosceles triangle opposite sides are equal, side B will also measure $12$. So far, the sum of the two opposite sides equals $24$. 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:

$30 - 24 = 6$.

Thus, the base will be equal to $6$.

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

Answer:

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

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

Answer:

Since in an isosceles triangle the opposite sides are equal, side A will also measure $10$. 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:

$37 - 20 = 7$

Thus, the length of the base is $7$.

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

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.

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.

$5 + 5 + 5 = 15$

Answer:

The perimeter of the triangle is equal to. $15$

Given the isosceles triangle:

The perimeter of the triangle is equal to $50$.

Task:

What is the value of $X$?

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 $X$, 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:

$X + X + 5.6 = 50$

$2X + 5.6 = 50$

We subtract the $5.6$

$2X = 44.4$

Divide by two

$X = 22.1$

Answer:

And we find that $X = 22.1$

Given the right triangle $\triangle ADB$

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

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

Task:

Calculate the area of the triangle. $\triangle ABC$

Solution:

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

From here we can calculate $AD$.

$AD + 5 + 13 = 30$

$AD + 18 = 30$

$AD = 12$

Now we can calculate the area of the triangle $ΔABC$

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

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

$A = \frac{altura\times base}{2}$

$A = \frac{AD \times BC}{2} = \frac{12 \times 4}{2} = \frac{48}{2} = 24$

Answer:

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

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

Task:

Which figure has the largest perimeter?

Solution:

In the beginning we will start with the triangle:

$P = AB + BC + CA$

$= AB + BC + CD + DA$

Using Pythagoras:

$CD² = BC² - BD² = 5² - 4² = 9$

We obtain its root

$CD = 3 \operatorname{cm}$

Again we use Pythagoras:

$AD² = AB² - BD² = 6² - 4² = 20$

We obtain its root

$AD = 4.47 \operatorname{cm}$

With the information obtained we calculate its perimeter.

$P = 6 + 5 + 3 + 4.47$

$= 18.47$

Now we move on to the circle:

$P = 2πR$

$= 2π \times 6$

$= 12π$

$= 12 \times 3.14$

$= 37.68$

Answer:

The perimeter of the circle is larger.

Given the triangle in the figure:

Homework:

What is its perimeter?

Solution:

Using Pythagoras

$AB² + BC² = AC²$

$49 + 9 = AC²$

$58 = AC²$

We obtain its root

$\sqrt{58} = AC$

We obtain the perimeter

$P = AB + BC + AC$

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

Answer:

$P = 10 + \sqrt{58}$

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 $ΔABC$, the formula is $P=AB+BC+CA$

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.

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

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.

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:

• Acute triangle
• Obtuse triangle
• Scalene Triangle
• Equilateral triangle
• Isosceles Triangle
• The edges of a triangle
• Area of a right triangle
• Height of a triangle
• How to calculate the area of a triangle
• How to calculate the perimeter of a triangle?

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

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