Which formula calculates the length of a hypotenuse?

The formula that calculates the length of a hypotenuse in a right triangle is derived from the Pythagorean theorem, which states that the sum of the squares of the two legs (a and b) of the triangle equals the square of the hypotenuse (c). This relationship is expressed as a² + b² = c².

When you know the lengths of the two legs, you can use this equation to solve for the hypotenuse. By rearranging the formula, one can find the hypotenuse by taking the square root of the sum of the squares of the other two sides. This principle is fundamental in carpentry and building construction, particularly when determining the diagonal measurements needed for structural supports and ensuring square corners.

The other formulas provided serve different purposes. The area of a triangle, the circumference of a circle, and a linear equation do not relate to the calculations required for determining the length of a hypotenuse in a right triangle. Thus, recognizing the Pythagorean theorem is crucial in the context of carpentry for achieving precise measurements.