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
- 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.
- Apply the Pythagorean theorem
According to the Pythagorean theorem, we need to check if
$$ 5^2 + 12^2 = 13^2 $$
- Calculate the squares
Calculate the squares of the lengths:
- $5^2 = 25$
- $12^2 = 144$
- $13^2 = 169$
- Sum the squares of the two shorter sides
Add the squares of the two shorter sides:
$$ 25 + 144 = 169 $$
- 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.
