Question

Consider a right-angled triangle with sides a = 6 and c = 9. Determine whether these values form a Pythagorean triple. Show
your steps and explain your answer. (2 points)


Write is 3 sentences in. 7th graders response

Answer 1

To see if the sides \(a = 6\) and \(c = 9\) can form a Pythagorean triple, we need to find the length of the other side, \(b\), using the Pythagorean theorem: \(a^2 + b^2 = c^2\). First, we calculate \(c^2\) which is \(9^2 = 81\), and \(a^2\) which is \(6^2 = 36\). Then, we can find \(b^2\) by rearranging the equation: \(b^2 = c^2 - a^2 = 81 - 36 = 45\), so \(b = \sqrt{45} \approx 6.7\); since \(b\) is not a whole number, the lengths \(6\), \(b\), and \(9\) do not form a Pythagorean triple.