Question

classifying triangles with known side lengths
which sets of three of numbers represent the sides of an obtuse triangle? choose two correct answers.
3, 4, 5
6, 8, 9
3, 5, 6
2, 2, 3
4, 7, 8
this question requires at least 2 answers.

Explanation:

Step1: Recall obtuse triangle rule

For a triangle with sides $a \leq b \leq c$, it is obtuse if $a^2 + b^2 < c^2$. First confirm each set satisfies triangle inequality (sum of two smaller sides > largest side, which all do here).

Step2: Test 3,4,5

$3^2 + 4^2 = 9 + 16 = 25 = 5^2$ → Right triangle, not obtuse.

Step3: Test 6,8,9

$6^2 + 8^2 = 36 + 64 = 100$; $9^2 = 81$. $100 > 81$ → Acute triangle.

Step4: Test 3,5,6

$3^2 + 5^2 = 9 + 25 = 34$; $6^2 = 36$. $34 < 36$ → Obtuse triangle.

Step5: Test 2,2,3

$2^2 + 2^2 = 4 + 4 = 8$; $3^2 = 9$. $8 < 9$ → Obtuse triangle.

Step6: Test 4,7,8

$4^2 + 7^2 = 16 + 49 = 65$; $8^2 = 64$. $65 > 64$ → Acute triangle.

Answer:

3, 5, 6
2, 2, 3