We will discuss here how to find the perimeter of a triangle. We know perimeter of a triangle is the total length (distance) of the boundary of a triangle.
Perimeter of a triangle is the sum of lengths of its three sides.
For example, perimeter of the ∆PQR = PQ + QR + RP
● The perimeter of a triangle ABC
= AB + BC + CA
= 2 cm + 4 cm + 3 cm,
(add the length of each side of the triangle).
= 9 cm
Perimeter of the triangle = Sum of the sides.
The perimeter of the triangle = Sum of the lengths of three sides.
Let us consider some of the examples on perimeter of a triangle:
1. Find the perimeter of a triangle having sides 3 cm, 8 cm and 6 cm.
Solution:
Perimeter of a triangle
= Sum of all the three sides
= AB + BC + AC
= 3 cm + 8 cm + 6 cm
= 17 cm
2. Find the perimeter of the triangle PQR whose sides are 4 cm, 6 cm and 8 cm.
Solution:
In the figure PQ = 4 cm, PR = 6 cm and QR = 8 cm
The perimeter of the rectangle PQR
= 4 cm + 6 cm + 8 cm
= 18 cm
3. Find the perimeter of an equilateral triangle whose one side is 5 cm.
Solution:
A triangle in which all the sides are equal is called an equilateral triangle.
Perimeter of the equilateral triangle = 3 × side
= 3 × 5 cm
= 15 cm
Thus, perimeter = 15 cm.
4. Find the perimeter of a triangle whose length of three sides are 8 cm, 11 cm, 13 cm.
Solution:
To find the perimeter of the triangle, we add all the sides together.
Perimeter of a triangle
= Sum of all the three sides
= 8 cm + 11 cm + 13 cm
= 32 cm
5. Find the perimeter of a triangle whose sides are 5 cm, 2 cm and 3 cm.
Solution:
Perimeter of the triangle is the sum of the lengths of its sides.
Perimeter = 5 cm + 2 cm + 3 cm
Thus, perimeter = 10 cm.
6. Find the perimeter of each triangle.
Solution:
(i) Perimeter of ∆XYZ = 5.5 cm + 6 cm + 6 cm = 17.5 cm
(ii) Perimeter of ∆ABC = 8 cm + 6 cm + 6 cm = 20 cm
(iii) Perimeter of ∆PQR = 4 cm + 3 cm + 5 cm = 12 cm
7. Find the perimeter of the given shapes.
Solution:
(i) Perimeter = PQ + QR + RS + ST + TU + UV + VP
= 2.5 cm + 3 cm + 2 cm + 3 cm + 2.5 cm + 4 cm + 4 cm
= 21 cm
(ii) Perimeter = PQ + QR + RS + SP
= 4 cm + 4 cm + 4 cm + 4 cm
= 16 cm
(iii) Perimeter = PQ + QR + RS + ST + TP
= 7 cm + 6 cm + 4 cm + 3 cm + 5 cm
= 25 cm
Word Problems on Perimeter of a Triangle:
1. Two sides of a triangle are 3 cm and 4 cm. Find the third side of the triangle if its perimeter is 11 cm.
Solution:
First side of the triangle = 3 cm
Second side of the triangle = 4 cm
Perimeter of the triangle = Sum of the lengths of sides
i.e. sum of the lengths of the sides = 11 cm
3 cm + 4 cm + length of the third side = 11 cm
7 cm + length of the third side = 11 cm
But we know that 7 cm + 4 cm = 11 cm (Note: 11 – 7 = 4)
Therefore, length of the third side = 4 cm
Questions and Answers on Perimeter of a Triangle:
1. A triangle has a perimeter of 50 cm. If its two sides are of lengths 15 cm and 19 cm, what is the length of the third side?
Answer: 16 cm
● Related Concepts
● To Measure the Length of a Line-segment
● Examples on Unit of Mass or Weight
● Units for The Measurement of Capacity
● Examples on Measurement of Capacity
● Antemeridian (a.m.) or Postmeridian (p.m.)
● Calendar
● Reading and Interpreting a Calendar
4th Grade Math Activities
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