Question

determine whether a triangle can be formed with the given side lengths.

1. 10 ft, 3 ft, 15 ft
2. 12 in., 4 in., 15 in.

Explanation:

Step1: Triangle inequality theorem

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

Step2: Solve for 5. \(10\mathrm{ft},3\mathrm{ft},15\mathrm{ft}\)

Here \(a = 3\), \(b = 10\), \(c=15\)
\(a + b=3 + 10=13\)
Since \(13<15\) (i.e. \(a + b

Step3: Solve for 6. \(12\mathrm{in},4\mathrm{in},15\mathrm{in}\)

Here \(a = 4\), \(b = 12\), \(c = 15\)
\(a + b=4+12 = 16\)
Since \(16>15\) (i.e. \(a + b>c\)), a triangle can be formed.

Answer:

1. No
2. Yes