Which equation expresses the Pythagorean theorem for a right triangle with legs a and b and hypotenuse c?

Which equation expresses the Pythagorean theorem for a right triangle with legs a and b and hypotenuse c?

• A. p = sum of all 3 sides
• B. a = 1/2 bh
• C. a^2 + b^2 = c^2
• D. a = l × w

Answer: (C)

In a right triangle, the square of the longest side (the hypotenuse) equals the sum of the squares of the other two sides. That idea is written as a^2 + b^2 = c^2. It matches the given letters because you square each leg, add them, and that result equals the square of the hypotenuse. For a quick check, if a = 3 and b = 4, then a^2 + b^2 = 9 + 16 = 25, so c^2 = 25 and c = 5. The other expressions correspond to different ideas: perimeter (p = sum of all three sides), triangle area (1/2 × base × height), and rectangle area (length × width).

In a right triangle, the square of the longest side (the hypotenuse) equals the sum of the squares of the other two sides. That idea is written as a^2 + b^2 = c^2. It matches the given letters because you square each leg, add them, and that result equals the square of the hypotenuse. For a quick check, if a = 3 and b = 4, then a^2 + b^2 = 9 + 16 = 25, so c^2 = 25 and c = 5.

The other expressions correspond to different ideas: perimeter (p = sum of all three sides), triangle area (1/2 × base × height), and rectangle area (length × width).