Question

classify each of the triangles as acute, obtuse, or right. triangle xyz is < triangle. triangle jkl is < triangle.

Explanation:

Step1: Recall the Pythagorean - related inequalities

For a triangle with side lengths \(a\), \(b\), and \(c\) where \(c\) is the longest side:

• If \(a^{2}+b^{2}=c^{2}\), the triangle is a right - triangle.
• If \(a^{2}+b^{2}>c^{2}\), the triangle is an acute - triangle.
• If \(a^{2}+b^{2}

Step2: Analyze triangle XYZ

In \(\triangle XYZ\), \(a = 4\), \(b = 4\), and \(c = 5\).
Calculate \(a^{2}+b^{2}\) and \(c^{2}\):
\(a^{2}+b^{2}=4^{2}+4^{2}=16 + 16=32\)
\(c^{2}=5^{2}=25\)
Since \(a^{2}+b^{2}=32>25 = c^{2}\), \(\triangle XYZ\) is an acute triangle.

Step3: Analyze triangle JKL

In \(\triangle JKL\), \(a = 3\), \(b = 4\), and \(c = 6\).
Calculate \(a^{2}+b^{2}\) and \(c^{2}\):
\(a^{2}+b^{2}=3^{2}+4^{2}=9 + 16=25\)
\(c^{2}=6^{2}=36\)
Since \(a^{2}+b^{2}=25<36 = c^{2}\), \(\triangle JKL\) is an obtuse triangle.

Answer:

Triangle XYZ is acute triangle.
Triangle JKL is obtuse triangle.