Question

indicate whether it is possible to create a triangle with each set of side lengths. side lengths yes 10 cm, 10 cm, 10 cm 2 cm, 7 cm, 13 cm 5.5 cm, 9.5 cm, 23 cm 8 cm, 8 cm, 12 cm 2 cm, 3 cm, 6 cm

Explanation:

Step1: Triangle inequality theorem

For three side lengths \(a\), \(b\), \(c\) (\(a\leq b\leq c\)), a triangle can be formed if \(a + b>c\)

Step2: Check \(2\mathrm{cm},7\mathrm{cm},13\mathrm{cm}\)

Here \(a = 2\), \(b = 7\), \(c=13\). Then \(a + b=2 + 7=9<13\)

Step3: Check \(5.5\mathrm{cm},9.5\mathrm{cm},23\mathrm{cm}\)

Here \(a = 5.5\), \(b = 9.5\), \(c = 23\). Then \(a + b=5.5+9.5 = 15<23\)

Step4: Check \(8\mathrm{cm},8\mathrm{cm},12\mathrm{cm}\)

Here \(a = 8\), \(b = 8\), \(c = 12\). Then \(a + b=8 + 8=16>12\)

Step5: Check \(2\mathrm{cm},3\mathrm{cm},6\mathrm{cm}\)

Here \(a = 2\), \(b = 3\), \(c = 6\). Then \(a + b=2+3 = 5<6\)

Answer:

For \(10\mathrm{cm},10\mathrm{cm},10\mathrm{cm}\): Yes; For \(2\mathrm{cm},7\mathrm{cm},13\mathrm{cm}\): No; For \(5.5\mathrm{cm},9.5\mathrm{cm},23\mathrm{cm}\): No; For \(8\mathrm{cm},8\mathrm{cm},12\mathrm{cm}\): Yes; For \(2\mathrm{cm},3\mathrm{cm},6\mathrm{cm}\): No