Question

use the pythagorean theorem to determine whether the following triangle is a right triangle. answer: yes because 18² = 17² - 6²; no because 18² ≠ 6² + 17²; no because 18 ≠ 17 + 6; yes because 18² = 17² + 6²

Explanation:

Step1: Recall Pythagorean Theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (the longest side) and \(a\) and \(b\) are the other two sides.
In this triangle, \(a = 6\), \(b = 17\), and \(c = 18\).
We need to check if \(6^{2}+17^{2}=18^{2}\).

Step2: Calculate left - hand side

Calculate \(6^{2}+17^{2}\):
\(6^{2}=6\times6 = 36\) and \(17^{2}=17\times17 = 289\).
So, \(6^{2}+17^{2}=36 + 289=325\).

Step3: Calculate right - hand side

Calculate \(18^{2}\):
\(18^{2}=18\times18 = 324\).
Since \(325
eq324\), i.e., \(6^{2}+17^{2}
eq18^{2}\).

Answer:

No because \(18^{2}
eq6^{2}+17^{2}\)