Which equation is equivalent to the Pythagorean formula A² + B² = C²?

Which equation is equivalent to the Pythagorean formula A² + B² = C²?

• A. A = square root (B² + C²)
• B. C = square root (A² + B²)
• C. square root (A² + B²) = C
• D. None of the above

Answer: (C)

The Pythagorean formula is expressed as A² + B² = C², where A and B represent the lengths of the legs of a right triangle, and C represents the length of the hypotenuse. To derive an equivalent equation, you can rearrange the original formula. In this case, if you take the original equation A² + B² = C² and isolate C, you get C = √(A² + B²). This is precisely what the option that states "square root (A² + B²) = C" conveys. Both expressions communicate the same relationship and are mathematically identical, which confirms that this option is an equivalent representation of the Pythagorean theorem. The other choices do not accurately reflect the relationships defined by the Pythagorean theorem. For instance, calculating the square root of the sum of the squares of B and C does not relate to the sides of a right triangle in this context, meaning that those equations do not fit the theorem's framework.

The Pythagorean formula is expressed as A² + B² = C², where A and B represent the lengths of the legs of a right triangle, and C represents the length of the hypotenuse. To derive an equivalent equation, you can rearrange the original formula.

In this case, if you take the original equation A² + B² = C² and isolate C, you get C = √(A² + B²). This is precisely what the option that states "square root (A² + B²) = C" conveys. Both expressions communicate the same relationship and are mathematically identical, which confirms that this option is an equivalent representation of the Pythagorean theorem.

The other choices do not accurately reflect the relationships defined by the Pythagorean theorem. For instance, calculating the square root of the sum of the squares of B and C does not relate to the sides of a right triangle in this context, meaning that those equations do not fit the theorem's framework.