Which equation could be used to find the length of the hypotenuse in a right triangle with legs of lengths $a$ and $b$?

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

Answer: (D)

Verified step by step guidance

1. Recall the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse length \(c\) is equal to the sum of the squares of the lengths of the two legs \(a\) and \(b\).
2. Write the Pythagorean theorem formula as \(c^{2} = a^{2} + b^{2}\), where \(c\) is the hypotenuse and \(a\), \(b\) are the legs.
3. Analyze the given options and compare each to the Pythagorean theorem formula to identify which one correctly represents the relationship.
4. Note that the equation \(c^{2} = a^{2} - b^{2}\) is incorrect because it subtracts the squares of the legs, which does not apply to right triangles.
5. Also, the equation \(c = a + b\) is incorrect because the hypotenuse is not simply the sum of the legs; it relates to their squares as per the Pythagorean theorem.