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题目

解题步骤

1. Understand the question

   practice classifying triangles with known side lengths.
   assignment
   which sets of three of numbers represent the sides of an obtuse triangle? check all that apply.
   □ 4,7,8
   □ 3,4,5
   □ 2,2,3
   □ 6,8,9
   □ 3,5,6

2. Explanation

   Step1: Recall obtuse triangle rule

   For sides $a \leq b \leq c$, triangle is obtuse if $a^2 + b^2 < c^2$, and must first satisfy triangle inequality $a + b > c$.

   Step2: Test set 4,7,8

   First, check triangle inequality: $4+7>8$ (11>8, true). Then calculate:
   $4^2 + 7^2 = 16 + 49 = 65$
   $8^2 = 64$
   $65 > 64$, so not obtuse.

   Step3: Test set 3,4,5

   Check triangle inequality: $3+4>5$ (7>5, true). Calculate:
   $3^2 + 4^2 = 9 + 16 = 25$
   $5^2 = 25$
   $25 = 25$, so right triangle, not obtuse.

   Step4: Test set 2,2,3

   Check triangle inequality: $2+2>3$ (4>3, true). Calculate:
   $2^2 + 2^2 = 4 + 4 = 8$
   $3^2 = 9$
   $8 < 9$, so obtuse.

   Step5: Test set 6,8,9

   Check triangle inequality: $6+8>9$ (14>9, true). Calculate:
   $6^2 + 8^2 = 36 + 64 = 100$
   $9^2 = 81$
   $100 > 81$, so not obtuse.

   Step6: Test set 3,5,6

   Check triangle inequality: $3+5>6$ (8>6, true). Calculate:
   $3^2 + 5^2 = 9 + 25 = 34$
   $6^2 = 36$
   $34 < 36$, so obtuse.

3. Final answer

   $\square$ 4,7,8
   $\square$ 3,4,5
   $\checkmark$ 2,2,3
   $\square$ 6,8,9
   $\checkmark$ 3,5,6

   Final selected sets: 2,2,3; 3,5,6

答案

Question Analysis

OCR Text

practice classifying triangles with known side lengths.
assignment
which sets of three of numbers represent the sides of an obtuse triangle? check all that apply.
□ 4,7,8
□ 3,4,5
□ 2,2,3
□ 6,8,9
□ 3,5,6

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