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practice classifying triangles with known side lengths. assignment whic…

$\square$ 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

Kategorie: geometry Aktualisiert: 2026-02-09

Aufgabe

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

Lösungsschritte

  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

Antwort

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.

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

Question Image

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Question Analysis

Subject mathematics
Sub Subject geometry
Education Level high school
Difficulty unspecified
Question Type multiple choice, calculation
Multi Question No
Question Count 1
Analysis Status completed
Analyzed At 2026-02-09T20:18:55

OCR Text

Show OCR extraction 
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

Verwandte Themen

mathematicsgeometrymultiple choice, calculationhigh schoolturns-1

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