Question 5 of 15beginner🔧 ApplyShort Answer4 marks
Check if a triangle exists for each of the following set of lengths: (a) 1, 100, 100 (b) 3, 6, 9 (c) 1, 1, 5 (d) 5, 10, 12
(a)
Answer
Triangle exists. Longest side 100 < 1 + 100 = 101.
(b)
Answer
No triangle exists. Longest side 9 = 3 + 6. Circles touch at one point, no triangle formed.
(c)
Answer
No triangle exists. Longest side 5 > 1 + 1 = 2.
(d)
Answer
Triangle exists. Longest side 12 < 5 + 10 = 15.
Explanation
(a) Triangle inequality satisfied. (b) When longest side equals sum of other two, circles touch but don't intersect. (c) Triangle inequality violated. (d) Triangle inequality satisfied.