Question

what is the formula for pythagorean theorem? a+b=c a-b=c c-a=c a²+b²=c²

Explanation:

Step1: Recall Pythagorean theorem

In a right - triangle, the sum of the squares of the two legs (\(a\) and \(b\)) equals the square of the hypotenuse (\(c\)).

Step2: Analyze options

• Option A: \(a + b=c\) is wrong. For example, if \(a = 3\), \(b=4\), \(a + b=7\), but in a right - triangle with legs \(3\) and \(4\), hypotenuse \(c = 5\).
• Option B: \(a - b=c\) is wrong. Since \(a,b,c>0\) and \(c>a,c > b\) in a right - triangle (where \(c\) is the hypotenuse), \(a - b=c\) would imply \(a>c\) which is false.
• Option C: \(c - a=c\) simplifies to \(a = 0\) which is not possible for a side of a triangle.
• Option D: \(a^{2}+b^{2}=c^{2}\) is the correct formula of the Pythagorean theorem. For a right - triangle with legs of lengths \(a\) and \(b\) and hypotenuse of length \(c\), by the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\). For example, when \(a = 3\), \(b = 4\), \(a^{2}+b^{2}=9 + 16=25\) and \(c^{2}=5^{2}=25\).

Answer:

D. \(a^{2}+b^{2}=c^{2}\)