Question

from which set of dimensions could a triangle be constructed?
side length of 2
side length of 6
side length of 7

side length of 8
side length of 5
side length of 14

side length of 6
side length of 3
side length of 10

side length of 7
side length of 8
side length of 15

Explanation:

Step1: Check triangle inequality for first set

For side lengths \(a = 2\), \(b=6\), \(c = 7\). Check \(a + b>c\), \(2+6 = 8>7\); \(a + c>b\), \(2 + 7=9>6\); \(b + c>a\), \(6+7 = 13>2\).

Step2: Check triangle inequality for second set

For side lengths \(a = 8\), \(b = 5\), \(c=14\). Check \(a + b>c\), \(8+5=13<14\).

Step3: Check triangle inequality for third set

For side lengths \(a = 6\), \(b = 3\), \(c = 10\). Check \(a + b>c\), \(6+3=9<10\).

Step4: Check triangle inequality for fourth set

For side lengths \(a = 7\), \(b = 8\), \(c = 15\). Check \(a + b>c\), \(7+8=15\) (not greater).

Answer:

side length of \(2\), side length of \(6\), side length of \(7\)