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

Answer: (B)

In a right triangle, the lengths are linked by the fact that the sum of the squares of the two legs equals the square of the hypotenuse. This means the relationship is expressed as a^2 + b^2 = c^2, where a and b are the legs and c is the hypotenuse. This form directly ties the two shorter sides to the longest side in a way that matches the geometric definition of the triangle’s right angle. Writing the same idea as c^2 = a^2 + b^2 is just a rearrangement and conveys the same essential link, but the standard convention places the sum of the leg squares on the left. The other options would misrepresent which sides are being squared and how they relate to the hypotenuse, so they don’t reflect the actual side-length relationship in a right triangle.

In a right triangle, the lengths are linked by the fact that the sum of the squares of the two legs equals the square of the hypotenuse. This means the relationship is expressed as a^2 + b^2 = c^2, where a and b are the legs and c is the hypotenuse. This form directly ties the two shorter sides to the longest side in a way that matches the geometric definition of the triangle’s right angle.

Writing the same idea as c^2 = a^2 + b^2 is just a rearrangement and conveys the same essential link, but the standard convention places the sum of the leg squares on the left. The other options would misrepresent which sides are being squared and how they relate to the hypotenuse, so they don’t reflect the actual side-length relationship in a right triangle.