Question

which of the following sets of lengths could be the sides of a triangle? (select all that apply) 37, 15, 22 10, 3, 11 15, 13, 14 30, 60, 25 7, 9, 12 25, 12, 10

Explanation:

Step1: Aplicar la desigualdad triangular

Para un triángulo con lados \(a\), \(b\) y \(c\), se debe cumplir que \(a + b>c\), \(a + c>b\) y \(b + c>a\).

Conjunto \(7,9,12\)

• \(7+9 = 16>12\)
• \(7 + 12=19>9\)
• \(9+12 = 21>7\)

Conjunto \(10,3,11\)

• \(3+10=13>11\)
• \(3 + 11=14>10\)
• \(10+11=21>3\)

Conjunto \(37,15,22\)

• \(15+22=37

ot>37\) (no cumple la desigualdad triangular)

Conjunto \(25,12,10\)

• \(10+12 = 22

ot>25\) (no cumple la desigualdad triangular)

Conjunto \(30,60,25\)

• \(25+30=55

ot>60\) (no cumple la desigualdad triangular)

Conjunto \(15,13,14\)

• \(13+14=27>15\)
• \(13 + 15=28>14\)
• \(14+15=29>13\)

Answer:

7,9,12; 10,3,11; 15,13,14