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In triangle XYZ, if side XY is 8 cm, side YZ is 6 cm, and side XZ is 10 cm, whic

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Question: In triangle XYZ, if side XY is 8 cm, side YZ is 6 cm, and side XZ is 10 cm, which of the following is true?

Options:

  1. It is a right triangle.
  2. It is an isosceles triangle.
  3. It is an equilateral triangle.
  4. It is a scalene triangle.

Correct Answer: It is a scalene triangle.

Solution: 

Since all sides are of different lengths, triangle XYZ is a scalene triangle.

In triangle XYZ, if side XY is 8 cm, side YZ is 6 cm, and side XZ is 10 cm, whic

Practice Questions

Q1
In triangle XYZ, if side XY is 8 cm, side YZ is 6 cm, and side XZ is 10 cm, which of the following is true?
  1. It is a right triangle.
  2. It is an isosceles triangle.
  3. It is an equilateral triangle.
  4. It is a scalene triangle.

Questions & Step-by-Step Solutions

In triangle XYZ, if side XY is 8 cm, side YZ is 6 cm, and side XZ is 10 cm, which of the following is true?
  • Step 1: Identify the lengths of the sides of triangle XYZ. They are XY = 8 cm, YZ = 6 cm, and XZ = 10 cm.
  • Step 2: Check if all sides are different lengths. Compare the lengths: 8 cm, 6 cm, and 10 cm.
  • Step 3: Since 8 cm is not equal to 6 cm, 8 cm is not equal to 10 cm, and 6 cm is not equal to 10 cm, all sides are different.
  • Step 4: Conclude that because all sides are of different lengths, triangle XYZ is a scalene triangle.
  • Triangle Classification – Understanding the classification of triangles based on the lengths of their sides (scalene, isosceles, equilateral).
  • Triangle Inequality Theorem – The theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
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