A triangle has sides of lengths 9 cm, 12 cm, and 15 cm. Is it a right triangle?

A triangle has sides of lengths 9 cm, 12 cm, and 15 cm. Is it a right triangle?

Step 1: Identify the lengths of the sides of the triangle. They are 9 cm, 12 cm, and 15 cm.
Step 2: Determine which side is the longest. The longest side is 15 cm.
Step 3: Use 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 4: Calculate the square of the longest side: 15 cm squared is 15² = 225.
Step 5: Calculate the square of the other two sides: 9 cm squared is 9² = 81 and 12 cm squared is 12² = 144.
Step 6: Add the squares of the two shorter sides: 81 + 144 = 225.
Step 7: Compare the sum from Step 6 with the square of the longest side from Step 4: 225 = 225.
Step 8: Since both sides are equal, 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 Inequality Theorem – A theorem that states the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.