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Worksheet: Equilateral Triangles

Q1:

One side of an equaliteral triangle has length ( 3 π‘₯ + 2 ) . Another side has length ( 7 π‘₯ βˆ’ 6 ) . Find the perimeter of the triangle.

Q2:

One side of an equaliteral triangle has length ( 4 π‘₯ + 7 ) . Another side has length ( 3 π‘₯ + 8 ) . Find the perimeter of the triangle.

Q3:

The perimeter of an equilateral triangle is equal to the perimeter of a rectangle with a length of 5 cm and a width of 4 cm. Find the length of one side of the triangle.

Q4:

The perimeter of an equilateral triangle is equal to the perimeter of a rectangle with a length of 12 cm and a width of 9 cm. Find the length of one side of the triangle.

Q5:

The diagram shows an equilateral triangle. Find the length of its sides.

Q6:

The diagram shows an equilateral triangle. Find the length of its sides.

Q7:

The diagram shows an equilateral triangle. Find the length of its sides.

Q8:

In the figure, find the values of π‘₯ and 𝑦 .

  • A π‘₯ = 2 0 , 𝑦 = 2 9
  • B π‘₯ = 3 2 , 𝑦 = 2 9
  • C π‘₯ = 3 2 , 𝑦 = 2 3
  • D π‘₯ = 2 0 , 𝑦 = 2 3

Q9:

In the figure, find the values of π‘₯ and 𝑦 .

  • A π‘₯ = 1 , 𝑦 = 1 3
  • B π‘₯ = 9 , 𝑦 = 1 3
  • C π‘₯ = 9 , 𝑦 = 7
  • D π‘₯ = 1 , 𝑦 = 7
  • E π‘₯ = 2 , 𝑦 = 7

Q10:

Calculate the length of one of the sides of an equilateral triangle which has a perimeter of 93 m.

Q11:

Given that triangle 𝐴 𝐡 𝐢 is equilateral, and 𝐴 𝐡 = 1 2 0 c m , determine the lengths of 𝐴 𝐢 and 𝐡 𝐢 .

  • A 60 cm, 60 cm
  • B 240 cm, 240 cm
  • C 120 cm, 240 cm
  • D 120 cm, 120 cm

Q12:

If one of the sides of an equilateral triangle measures 50 cm, calculate its perimeter.

Q13:

A triangle has three sides equal in length and a perimeter of 24 length units. Find the length of one of its sides.

Q14:

If a square with side length 54 cm has the same perimeter as an equilateral triangle, what is the side length of the triangle?

Q15:

Find the value of ∠ π‘Œ given 𝑋 π‘Œ 𝑍 is a triangle where 𝑋 π‘Œ = π‘Œ 𝑍 = 𝑍 𝑋 = 6 c m .

Q16:

What is the ratio of the length of a side of an equilateral triangle to its perimeter?

  • A 3 ∢ 1
  • B 1 ∢ 1
  • C 1 ∢ 2
  • D 1 ∢ 3
  • E 2 ∢ 1

Q17:

What is the size of each angle in an equilateral triangle?

  • A
  • B
  • C
  • D

Q18:

From a deck of cards that has a length of 7 2 inches, you take two cards and lean them together to create an equilateral triangle. What is the height of the triangle?

  • A 7 √ 3 6 inches
  • B 7 4 inches
  • C 7 √ 3 2 inches
  • D 7 √ 3 4 inches
  • E 7 √ 2 2 inches

Q19:

In β–³ 𝑋 π‘Œ 𝑍 , if 𝑋 π‘Œ = π‘Œ 𝑍 = 𝑋 𝑍 , then π‘š ∠ 𝑍 = .

Q20:

In the figure below, is an equilateral triangle, , and . Find .

  • A
  • B
  • C
  • D

Q21:

In the figure below, is an equilateral triangle, , and . Find .

  • A
  • B
  • C
  • D

Q22:

In β–³ 𝑋 π‘Œ 𝑍 , if 𝑋 π‘Œ = π‘Œ 𝑍 = 𝑋 𝑍 , then π‘š ∠ π‘Œ = .

  • A 8 0 ∘
  • B 3 0 ∘
  • C 4 5 ∘
  • D 6 0 ∘

Q23:

Find the perimeter of β–³ 𝐴 𝐡 𝐢 .

Q24:

The area of an equilateral triangle is 2 5 6 √ 3 cm2. Find the side length.

Q25:

The area of an equilateral triangle is 2 5 √ 3 cm2. Find the side length.