Which mathematical equation can be used to determine if a triangle with side lengths $a$, $b$, and $c$ (where $c$ is the longest side) is a right triangle?

• A. $a^2+b^2=c^3$
• B. $a^2+b^2=c^2$
• C. $a^2-b^2=c^2$
• D. $a+b=c$

Answer: (B)

Verified step by step guidance

1. Recall the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
2. Identify the sides of the triangle: let \( a \) and \( b \) be the lengths of the two shorter sides, and \( c \) be the length of the longest side (hypotenuse).
3. Write the Pythagorean theorem equation as: \( a^{2} + b^{2} = c^{2} \).
4. To determine if the triangle is right-angled, check if the given side lengths satisfy the equation \( a^{2} + b^{2} = c^{2} \).
5. If the equation holds true, the triangle is right-angled; if not, it is not a right triangle.