Question 1 - Figure it out - Page 159 - Chapter 7 Class 7 - A tale of three Intersecting Lines (Ganit Prakash)

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Question 1 Check if a triangle exists for each of the following set of lengths: 1, 100, 100 (b) 3, 6, 9 (c) 1, 1, 5 (d) 5, 10, 12 We need to check Triangle Inequality Which says Sum of Two Sides > Third Side We don’t need to check all the combinations We just check if Sum of smaller sides > Largest side Let’s do this one by one (a) 1, 100, 100 Here, Sum of smaller two sides = 1 + 100 = 101 And, Largest side = 100 Now, 101 > 100 This satisfies triangle inequality ∴ Triangle exists (b) 3, 6, 9 Here, Sum of smaller two sides = 3 + 6 = 9 And, Largest side = 9 Now, 9 = 9 This does not satisfy triangle inequality ∴ Triangle does not exist (c) 1, 1, 5 Here, Sum of smaller two sides = 1 + 1 = 2 And, Largest side = 5 Now, 2 < 5 This does not satisfy triangle inequality ∴ Triangle does not exist (d) 5, 10, 12 Here, Sum of smaller two sides = 5 + 10 = 15 And, Largest side = 12 Now, 15 > 12 This satisfies triangle inequality ∴ Triangle exists