If a triangle has sides of lengths 3, 4, and 5, what type of triangle is it?

If a triangle has sides of lengths 3, 4, and 5, what type of triangle is it?

Step 1: Identify the lengths of the sides of the triangle. Here, the sides are 3, 4, and 5.
Step 2: Recall the Pythagorean theorem, which states that in a right triangle, the square of the length of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides.
Step 3: Determine which side is the longest. In this case, 5 is the longest side.
Step 4: Calculate the squares of the sides: 3^2 = 9, 4^2 = 16, and 5^2 = 25.
Step 5: Check if the Pythagorean theorem holds: 9 + 16 = 25. Since this is true, the triangle is a right triangle.

Triangle Classification – Understanding how to classify triangles based on the lengths of their sides, including right, acute, and obtuse triangles.
Pythagorean Theorem – Applying the Pythagorean theorem (a² + b² = c²) to determine if a triangle is a right triangle.