🎧 New: AI-Generated Podcasts Turn your study notes into engaging audio conversations. Learn more

Is 5, 12, 13 a right triangle?

Understand the Problem

The question is asking whether the sides measuring 5, 12, and 13 can form a right triangle. To determine this, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. Here, we would check if 5² + 12² equals 13².

Answer

Yes, the sides 5, 12, and 13 can form a right triangle.
Answer for screen readers

Yes, the sides 5, 12, and 13 can form a right triangle.

Steps to Solve

  1. Identify the sides and the hypotenuse

Identify the sides of the triangle. Here, the sides are 5 and 12, and we will consider 13 as the hypotenuse.

  1. Apply the Pythagorean theorem

According to the Pythagorean theorem, we need to check if

$$ 5^2 + 12^2 = 13^2 $$

  1. Calculate the squares

Calculate the squares of the lengths:

  • $5^2 = 25$
  • $12^2 = 144$
  • $13^2 = 169$
  1. Sum the squares of the two shorter sides

Add the squares of the two shorter sides:

$$ 25 + 144 = 169 $$

  1. Compare with the square of the hypotenuse

Now, check if the sum equals the square of the hypotenuse:

$$ 169 = 169 $$

Since both sides of the equation are equal, the triangle is indeed a right triangle.

Yes, the sides 5, 12, and 13 can form a right triangle.

More Information

The combination of the lengths 5, 12, and 13 is one of the classic examples of a Pythagorean triple. Pythagorean triples are sets of three positive integers that satisfy the Pythagorean theorem and have been studied for their unique properties.

Tips

  • A common mistake is to misidentify which side is the hypotenuse. Always ensure the longest side is treated as the hypotenuse.
  • Another mistake is calculating the squares incorrectly. Double-check basic calculations.
Thank you for voting!
Use Quizgecko on...
Browser
Browser