Question

is it possible to construct a triangle with the given side lengths? if not, explain why not 7 6, 10, 16 8 11,16,32 9 3, 5, 8

Explanation:

7. Check if \(6\), \(10\), \(16\) can form a triangle

Step1: Apply triangle - inequality theorem (sum of two sides must be greater than the third side)

Check \(6 + 10>16\).
\(6+10 = 16\), and \(16
ot>16\).

8. Check if \(11\), \(16\), \(32\) can form a triangle

Step1: Apply triangle - inequality theorem

Check \(11 + 16>32\).
\(11 + 16=27\), and \(27
ot>32\).

9. Check if \(3\), \(5\), \(8\) can form a triangle

Step1: Apply triangle - inequality theorem

Check \(3 + 5>8\).
\(3 + 5 = 8\), and \(8
ot>8\).

Answer:

1. No, because \(6 + 10=16\) (violates the triangle - inequality theorem).
2. No, because \(11 + 16 = 27<32\) (violates the triangle - inequality theorem).
3. No, because \(3 + 5=8\) (violates the triangle - inequality theorem).