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題目

解題步驟

1. Understand the question

   applying the triangle inequality theorems and the converse of the pythagorean theorem
   classify each of the triangles as acute, obtuse, or right.
   triangle jkl is □ triangle.
   triangle xyz is □ triangle.
   triangle jkl has side lengths: jk=4, jl=6, kl=3
   triangle xyz has side lengths: xz=4, zy=4, xy=5

2. Explanation

   Step1: Classify △JKL

   Let \(a=3\), \(b=4\), \(c=6\) (longest side).
   Compare \(a^2 + b^2\) vs \(c^2\):
   \(3^2 + 4^2 = 9 + 16 = 25\)
   \(6^2 = 36\)
   Since \(25 < 36\), \(a^2 + b^2 < c^2\).

   Step2: Classify △XYZ

   Let \(a=4\), \(b=4\), \(c=5\) (longest side).
   Compare \(a^2 + b^2\) vs \(c^2\):
   \(4^2 + 4^2 = 16 + 16 = 32\)
   \(5^2 = 25\)
   Since \(32 > 25\), \(a^2 + b^2 > c^2\).

3. Final answer

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

答案

Question Analysis

OCR Text

applying the triangle inequality theorems and the converse of the pythagorean theorem
classify each of the triangles as acute, obtuse, or right.
triangle jkl is □ triangle.
triangle xyz is □ triangle.
triangle jkl has side lengths: jk=4, jl=6, kl=3
triangle xyz has side lengths: xz=4, zy=4, xy=5

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