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If a triangle has sides of lengths 5, 12, and 13, what type of triangle is it?

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Question: If a triangle has sides of lengths 5, 12, and 13, what type of triangle is it?

Options:

  1. Acute
  2. Obtuse
  3. Right
  4. Equilateral

Correct Answer: Right

Solution: 

A triangle with sides a, b, and c (where c is the longest side) is a right triangle if a² + b² = c². Here, 5² + 12² = 25 + 144 = 169 = 13², so it is a right triangle.

If a triangle has sides of lengths 5, 12, and 13, what type of triangle is it?

Practice Questions

Q1
If a triangle has sides of lengths 5, 12, and 13, what type of triangle is it?
  1. Acute
  2. Obtuse
  3. Right
  4. Equilateral

Questions & Step-by-Step Solutions

If a triangle has sides of lengths 5, 12, and 13, what type of triangle is it?
  • Step 1: Identify the lengths of the sides of the triangle. Here, the sides are 5, 12, and 13.
  • Step 2: Determine which side is the longest. The longest side is 13.
  • Step 3: Label the sides as a, b, and c, where c is the longest side. Let a = 5, b = 12, and c = 13.
  • Step 4: Use the Pythagorean theorem, which states that a triangle is a right triangle if a² + b² = c².
  • Step 5: Calculate a². This is 5² = 25.
  • Step 6: Calculate b². This is 12² = 144.
  • Step 7: Add a² and b² together. This is 25 + 144 = 169.
  • Step 8: Calculate c². This is 13² = 169.
  • Step 9: Compare the results from Step 7 and Step 8. Since 169 = 169, the triangle is a right triangle.
  • Pythagorean Theorem – A theorem that states in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
  • Triangle Classification – Triangles can be classified based on their side lengths and angles, including right, acute, and obtuse triangles.
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