Worksheet: Perimeter of a Triangle

In this worksheet, we will practice finding the perimeter of a triangle as a value and as an algebraic expression by adding its side lengths.

Q1:

What is the perimeter of this triangle?

Q2:

Write an expression in terms of 𝑥 , for the perimeter in cm, of the isosceles triangle shown below.

  • A 2 0 𝑥 cm
  • B 1 0 𝑥 cm
  • C ( 𝑥 + 1 0 ) cm
  • D ( 2 𝑥 + 1 0 ) cm

Q3:

The base of an isosceles triangle is 4 more than the length of one of the equal sides. Let 𝑙 be the length of one of the equal sides and write an equation for 𝑃 , the perimeter of the triangle.

  • A 𝑃 = 4 𝑙 + 3
  • B 𝑃 = 2 𝑙 + 4
  • C 𝑃 = 2 𝑙 + 3
  • D 𝑃 = 3 𝑙 + 4
  • E 𝑃 = 4 𝑙 + 2

Q4:

Calculate the perimeter of an equilateral triangle whose side length is 3.39 cm.

Q5:

In the parallelogram shown, 𝐵 𝑀 = 3 8 and 𝑀 𝐶 = 5 4 . What is the perimeter of 𝐴 𝑀 𝐷 ?

Q6:

If the perimeter of this triangle is 234, find the length of the third side.

Q7:

The perimeter of a triangular piece of land is 166 meters. Find the length of its third side if the sum of two of its sides is 102 meters.

Q8:

The side length of an equilateral triangle is 8 𝑥 units and its perimeter is 𝑝 units. Write the mathematical relation between 𝑝 and 𝑥 .

  • A 𝑝 = 3 2 𝑥
  • B 𝑝 = 1 1 𝑥
  • C 𝑝 = 1 2 𝑥
  • D 𝑝 = 2 4 𝑥
  • E 𝑝 = 8 𝑥 + 3

Q9:

Given that 𝐷 𝐹 = 1 0 0 c m and 𝑋 𝑍 = 2 2 c m , find the perimeter of 𝐷 𝐸 𝑍 to the nearest hundredth, if needed.

Q10:

Find the perimeters of 𝐴 𝐵 𝐶 and 𝐵 𝐶 𝐷 .

  • A perimeter of 𝐴 𝐵 𝐶 = 1 5 c m , perimeter of 𝐵 𝐶 𝐷 = 1 5 c m
  • B perimeter of 𝐴 𝐵 𝐶 = 2 2 c m , perimeter of 𝐵 𝐶 𝐷 = 2 3 . 5 6 c m
  • C perimeter of 𝐴 𝐵 𝐶 = 2 8 . 5 c m , perimeter of 𝐵 𝐶 𝐷 = 3 1 . 5 c m
  • D perimeter of 𝐴 𝐵 𝐶 = 4 2 c m , perimeter of 𝐵 𝐶 𝐷 = 4 8 c m

Q11:

Find the perimeter of 𝐴 𝐵 𝐶 .

Q12:

𝐴 𝐵 𝐶 is a triangle where 𝑏 = 2 8 c m , 𝑎 + 𝑐 = 4 9 c m and 𝑎 𝑐 = 3 c m . Find the perimeter of the triangle giving the answer to the nearest centimetre.

Q13:

𝐴 𝐵 𝐶 is a triangle, where 𝐵 𝐶 = 5 5 cm, 𝐴 𝐶 𝐴 𝐵 = 1 3 cm, and the perimeter is 124 cm. Find the lengths of 𝐴 𝐶 and 𝐴 𝐵 giving the answers to the nearest centimetre.

  • A 𝐴 𝐶 = 2 8 c m , 𝐴 𝐵 = 4 1 c m
  • B 𝐴 𝐶 = 4 1 c m , 𝐴 𝐵 = 5 4 c m
  • C 𝐴 𝐶 = 1 5 c m , 𝐴 𝐵 = 2 8 c m
  • D 𝐴 𝐶 = 4 1 c m , 𝐴 𝐵 = 2 8 c m
  • E 𝐴 𝐶 = 9 6 c m , 𝐴 𝐵 = 2 8 c m

Q14:

The perimeter of a triangle is given by 𝑥 + 5 𝑥 + 1 cm. The lengths of two of its sides are 8 𝑥 + 𝑥 cm and 3 𝑥 + 4 cm. Express the length of the third side in terms of 𝑥 .

  • A 7 𝑥 + 3 𝑥 + 5 cm
  • B 9 𝑥 + 7 𝑥 3 cm
  • C 7 𝑥 + 3 𝑥 + 5 cm
  • D 9 𝑥 + 7 𝑥 3 cm

Q15:

In triangle 𝐴 𝐵 𝐶 we have 𝐴 𝐵 = 𝐴 𝐶 and 𝑚 𝐶 = 6 0 . If the perimeter of the triangle is 46.2, what is the length of 𝐵 𝐶 ?

Q16:

Determine the perimeter of the triangle whose sides have the same length of 22 cm.

Q17:

What is the range of possible perimeters, 𝑃 , of the given figure 𝐴 𝐵 𝐶 𝐷 𝐸 if 𝐴 𝐶 = 5 and 𝐷 𝐶 = 9 ?

  • A 1 9 < 𝑃 < 2 3
  • B 1 8 < 𝑃 < 2 8
  • C 𝑃 > 1 8
  • D 3 6 < 𝑃 < 5 6
  • E 𝑃 < 5 6

Q18:

Find the perimeter of a triangle whose side lengths are 7, 25, and 22.

Q19:

Find the perimeter of a triangle whose side lengths are 8 cm, 10 cm, and 4 cm.

Q20:

A triangle of perimeter 37 has two sides of lengths 11 and 8. What is the length of the third side?

Q21:

Calculate the perimeter of the triangle.

Q22:

A triangular fountain has a perimeter of 123 feet. If one of its sides is 32 feet long, and another is 57 feet long, determine the length of its third side.

Q23:

What is the perimeter of triangle 𝐴 𝐵 𝐶 , given that 𝐴 𝐵 = 3 , 𝐵 𝐶 = 5 , and 𝐶 𝐴 = 7 ?

Q24:

A triangle has a perimeter of 44. If two of the sides have lengths 19 and 13, what is the length of the third side?

Q25:

Determine the perimeter of the triangle 𝐴 𝐵 𝐶 , given that 𝐴 𝐵 = 1 0 c m , 𝐵 𝐶 = 7 c m , and 𝐴 𝐶 = 6 c m .

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