Question

If a triangle has side lengths 5 cm, 18
cm, and 12 cm, is it a right triangle?

Answer 1

No, it's not a right triangle.

Explanation:

1. The Pythagorean Theorem states that the area of the square whose side is the hypotenuse (longest side of a right triangle) is equal to the sum of the area of the squares from the two other sides.

2. The longest side in this "triangle" has 18 centimeters, and the other 2 sides are 5 and 12 centimeters.

3. Let's apply the Pythagorean Theorem to see if 5^2 + 12^2 = 18^2

• 
  `5^2 + 12^2 = 18^2`
• 
  `25 + 144 = 324`
• 
  `169 \\eq 324`

4. Okay, so the sum of the area of the squares from the two other sides is not equal to the hypotenuse squared, therefore, it's not a right triangle.

(Plus, it's not even a triangle because 7 < x < 17, and the third "side", 18, is not between 7 and 17.)