Question

question 12 of 28 which of the following statements justifies why the triangle shown below is not a right triangle? a. bc + ac < ab b. ac < ab c. bc < ab d. 6²+11²≠15²

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with sides \(a\), \(b\), and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). In \(\triangle ABC\), if it were a right - triangle, and assuming the longest side \(AB = 15\) is the hypotenuse, then for sides \(BC = 6\) and \(AC = 11\), we should have \(BC^{2}+AC^{2}=AB^{2}\).

Step2: Check the Pythagorean condition

Calculate \(BC^{2}+AC^{2}\) and \(AB^{2}\). \(BC^{2}=6^{2}=36\), \(AC^{2}=11^{2}=121\), so \(BC^{2}+AC^{2}=36 + 121=157\). And \(AB^{2}=15^{2}=225\). Since \(6^{2}+11^{2}
eq15^{2}\), the triangle is not a right - triangle.

Answer:

D. \(6^{2}+11^{2}
eq15^{2}\)