Question

1. reasoning can sticks of lengths 3 inches, 4 inches, and 6 inches be sides of a right triangle? justify your answer.

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, the Pythagorean theorem states that \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side (hypotenuse) and \(a\), \(b\) are the other two sides.
Here, the sides are 3, 4, 6. The longest side \(c = 6\), and \(a = 3\), \(b = 4\).

Step2: Calculate \(a^{2}+b^{2}\) and \(c^{2}\)

Calculate \(a^{2}+b^{2}\): \(3^{2}+4^{2}=9 + 16=25\)
Calculate \(c^{2}\): \(6^{2}=36\)

Step3: Compare the two results

Since \(25
eq36\) (i.e., \(3^{2}+4^{2}
eq6^{2}\)), the Pythagorean theorem is not satisfied.

Answer:

No, sticks of lengths 3 inches, 4 inches, and 6 inches cannot be sides of a right triangle because \(3^{2}+4^{2}=25\) and \(6^{2} = 36\), and \(25
eq36\) (the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) for a right triangle is not satisfied).