If a triangle has sides of lengths 5 cm, 12 cm, and 13 cm, what type of triangle

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

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

Step 1: Identify the lengths of the sides of the triangle. They are 5 cm, 12 cm, and 13 cm.
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: Identify the longest side. In this case, the longest side is 13 cm.
Step 4: Calculate the square of each side: 5² = 25, 12² = 144, and 13² = 169.
Step 5: Add the squares of the two shorter sides: 25 + 144 = 169.
Step 6: Compare the sum to the square of the longest side: 169 (from the shorter sides) equals 169 (from the longest side).
Step 7: Since the equation 5² + 12² = 13² holds true, the triangle is a right triangle.

Pythagorean Theorem – A mathematical principle 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.
Types of Triangles – Triangles can be classified based on their angles (acute, right, obtuse) or their sides (scalene, isosceles, equilateral).