Question

answer the question correctly to continue: which triangle has sides that satisfy the pythagorean theorem? 2, 3, 4 5, 6, 8 3, 4, 5 6, 7, 10

Explanation:

Step1: Recall Pythagorean Theorem

The Pythagorean Theorem states that for a right - triangle with sides \(a\), \(b\) (legs) and \(c\) (hypotenuse), \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side.

Step2: Check each set of sides

• For \(2,3,4\): \(2^{2}+3^{2}=4 + 9=13\), \(4^{2}=16\). Since \(13

eq16\), this does not satisfy the theorem.

• For \(5,6,8\): \(5^{2}+6^{2}=25 + 36=61\), \(8^{2}=64\). Since \(61

eq64\), this does not satisfy the theorem.

• For \(3,4,5\): \(3^{2}+4^{2}=9 + 16=25\), \(5^{2}=25\). Since \(25 = 25\), this satisfies the theorem.
• For \(6,7,10\): \(6^{2}+7^{2}=36+49 = 85\), \(10^{2}=100\). Since \(85

eq100\), this does not satisfy the theorem.

Answer:

\(3,4,5\)