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Solution Steps

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

Answer

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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