Perimeter of the triangle - Examples, Exercises and Solutions

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

Suggested Topics to Practice in Advance

  1. Area
  2. The Sum of the Interior Angles of a Triangle
  3. The sides or edges of a triangle
  4. Triangle Height
  5. Exterior angles of a triangle
  6. Types of Triangles
  7. Obtuse Triangle
  8. Equilateral triangle
  9. Identification of an Isosceles Triangle
  10. Scalene triangle
  11. Acute triangle
  12. Isosceles triangle
  13. The Area of a Triangle
  14. Area of a right triangle
  15. Area of Isosceles Triangles
  16. Area of a Scalene Triangle
  17. Area of Equilateral Triangles

Practice Perimeter of the triangle

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

examples with solutions for perimeter of the triangle

Exercise #1

Below is an equilateral triangle:

XXX

If the perimeter of the triangle is 33 cm, then what is the value of X?

Video Solution

Step-by-Step Solution

We know that in an equilateral triangle all sides are equal.

Therefore, if we know that one side is equal to X, then all sides are equal to X.

We know that the perimeter of the triangle is 33.

The perimeter of the triangle is equal to the sum of the sides together.

We replace the data:

x+x+x=33 x+x+x=33

3x=33 3x=33

We divide the two sections by 3:

3x3=333 \frac{3x}{3}=\frac{33}{3}

x=11 x=11

Answer

11

Exercise #2

Below is the right triangle ABD, which has a perimeter of 36 cm.

AB = 15

AC = 13

DC = 5

CB = 4

Work out the area of the triangle.

151515444555131313BBBCCCDDDAAA

Video Solution

Step-by-Step Solution

According to the data:

BD=4+5=9 BD=4+5=9

Now that we are given the perimeter of triangle ABD we can find the missing side AD:

AD+15+9=36 AD+15+9=36

AD+24=36 AD+24=36

AD=3624=12 AD=36-24=12

Now we can calculate the area of triangle ABD:

AD×BD2=12×92=1082=54 \frac{AD\times BD}{2}=\frac{12\times9}{2}=\frac{108}{2}=54

Answer

54 cm²

Exercise #3

The triangle ABC has a perimeter measuring 42 cm.

AD = 12

AC = 15

AB = 13

Calculate the area of the triangle.

131313151515121212AAABBBCCCDDD

Video Solution

Step-by-Step Solution

Given that the perimeter of triangle ABC is 42.

We will use this data to find side CB:

13+15+CB=42 13+15+CB=42

CB+28=42 CB+28=42

CB=4228=14 CB=42-28=14

Now we can calculate the area of triangle ABC:

AD×BC2=12×142=1682=84 \frac{AD\times BC}{2}=\frac{12\times14}{2}=\frac{168}{2}=84

Answer

84 cm²

Exercise #4

Look at the isosceles triangle below:

5.65.65.6XXX

The perimeter of the triangle is 50.

What is the value of X?

Video Solution

Step-by-Step Solution

Since we know the triangle is isosceles, the other side will also be equal to X

Now we can replace the data to calculate X.

The perimeter of the triangle is equal to:

x+x+5.6=50 x+x+5.6=50

2x=505.6 2x=50-5.6

2x=44.4 2x=44.4

We divide both sides by 2:

2x2=44.42 \frac{2x}{2}=\frac{44.4}{2}

x=22.2 x=22.2

Answer

22.2

Exercise #5

Look at the following triangle:

2X2X2X3.5X3.5X3.5X3X3X3X

The perimeter of the triangle is 17.

What is the value of X?

Video Solution

Step-by-Step Solution

We know that the perimeter of a triangle is equal to the sum of all sides together, so we replace the data:

3x+2x+3.5x=17 3x+2x+3.5x=17

8.5x=17 8.5x=17

Divide the two sections by 8.5:

8.5x8.5=178.5 \frac{8.5x}{8.5}=\frac{17}{8.5}

x=2 x=2

Answer

2

examples with solutions for perimeter of the triangle

Exercise #1

Look at the triangle in the figure.

What is its perimeter?

777333AAABBBCCC

Video Solution

Step-by-Step Solution

To find the perimeter of a triangle, first we need to find all its sides.

Given two sides and only the perimeter remains to be found.

We can use the Pythagorean Theorem
AB2+BC2=AC2 AB^2+BC^2=AC^2
We replace all the known data:

AC2=72+32 AC^2=7^2+3^2
AC2=49+9=58 AC^2=49+9=58
We extract the square root:

AC=58 AC=\sqrt{58}
Now that we have all the sides, we can add them up and thus find the perimeter:
58+7+3=58+10 \sqrt{58}+7+3=\sqrt{58}+10

Answer

10+58 10+\sqrt{58} cm

Exercise #2

The perimeter of the triangle ABD shown below is 36 cm.

Given in cm:

AB = 15

AC = 13

DC = 5

CB = 4

Calculate the area of triangle ADC.

151515131313AAABBBDDDCCC54

Video Solution

Step-by-Step Solution

We use the data of the triangle's perimeter, with the help of which we will first find the side AD by calculating the sum of all the sides of the triangle:

AD+9+15=36 AD+9+15=36

AD+24=36 AD+24=36

AD=3624=12 AD=36-24=12

Now that we know that AD is equal to 12, we will note that AD is also the height from BD since it forms a 90-degree angle.

If AD is the height from BD, it is also the height from DC.

Now we calculate the area of the triangle ADC:

AD×DC2 \frac{AD\times DC}{2}

12×52=602=30 \frac{12\times5}{2}=\frac{60}{2}=30

Answer

30 cm²

Exercise #3

Look at the triangle in the figure.

What is the length of the hypotenuse given that its perimeter is 12+45 12+4\sqrt{5} cm?

444AAABBBCCC

Video Solution

Step-by-Step Solution

We calculate the perimeter of the triangle:

12+45=4+AC+BC 12+4\sqrt{5}=4+AC+BC

As we want to find the hypotenuse (BC), we isolate it:

12+454AC=BC 12+4\sqrt{5}-4-AC=BC

BC=8+45AC BC=8+4\sqrt{5}-AC

Then calculate AC using the Pythagorean theorem:

AB2+AC2=BC2 AB^2+AC^2=BC^2

42+AC2=(8+45AC)2 4^2+AC^2=(8+4\sqrt{5}-AC)^2

16+AC2=(8+45)22×AC(8+45)+AC2 16+AC^2=(8+4\sqrt{5})^2-2\times AC(8+4\sqrt{5})+AC^2

We then simplify the two:AC2 AC^2

16=82+2×8×45+(45)22×8×AC2AC45 16=8^2+2\times8\times4\sqrt{5}+(4\sqrt{5})^2-2\times8\times AC-2AC4\sqrt{5}

16=64+645+16×516AC85AC 16=64+64\sqrt{5}+16\times5-16AC-8\sqrt{5}AC

16AC+85AC=64+645+16×516 16AC+8\sqrt{5}AC=64+64\sqrt{5}+16\times5-16

AC(16+85)=128+645 AC(16+8\sqrt{5})=128+64\sqrt{5}

AC=128+64516+85=8(16+85)16+85 AC=\frac{128+64\sqrt{5}}{16+8\sqrt{5}}=\frac{8(16+8\sqrt{5})}{16+8\sqrt{5}}

We simplify to obtain:

AC=8 AC=8

Now we can replace AC with the value we found for BC:

BC=8+45AC BC=8+4\sqrt{5}-AC

BC=8+458=45 BC=8+4\sqrt{5}-8=4\sqrt{5}

Answer

45 4\sqrt{5} cm

Exercise #4

Find the perimeter of the triangle ABC

333444555AAABBBCCC

Video Solution

Answer

12

Exercise #5

Find the perimeter of the triangle ABC

777141414888AAABBBCCC

Video Solution

Answer

29

Topics learned in later sections

  1. Perimeter
  2. Triangle