Question

decide whether it is possible to construct a triangle with the given side lengths. explain your reasoning. 7. 4 ft, 9 ft, 10 ft 8. 8 m, 9 m, 18 m 9. 5 cm, 7 cm, 12 cm

Explanation:

7. 4 ft, 9 ft, 10 ft

Step1: Comprobar la desigualdad triangular para los lados \(a = 4\), \(b=9\), \(c = 10\)

La desigualdad triangular dice que \(a + b>c\), \(a + c>b\) y \(b + c>a\)

• \(a + b=4 + 9=13>10\)
• \(a + c=4+10 = 14>9\)
• \(b + c=9 + 10=19>4\)

8. 8 m, 9 m, 18 m

Step1: Comprobar la desigualdad triangular para los lados \(a = 8\), \(b = 9\), \(c=18\)

• \(a + b=8 + 9=17<18\)

9. 5 cm, 7 cm, 12 cm

Step1: Comprobar la desigualdad triangular para los lados \(a = 5\), \(b = 7\), \(c = 12\)

• \(a + b=5+7 = 12

ot>12\)

Answer:

1. Sí, porque \(4 + 9>10\), \(4+10>9\) y \(9 + 10>4\)
2. No, porque \(8 + 9<18\)
3. No, porque \(5 + 7=12\)