Which of the following lengths can be the sidelengths of a triangle? - Figure it out - Page 156

part 2 - Question (a) - Figure it out - Page 156 - Chapter 7 Class 7 - A tale of three Intersecting Lines (Ganit Prakash) - Class 7 (Ganita Prakash 1, 2 & old NCERT)

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Question (a) Which of the following lengths can be the sidelengths of a triangle? Explain your answers. Note that for each set, the three lengths have the same unit of measure. (a) 2, 2, 5 We will check this using 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 Here, Sum of smaller two sides = 2 + 2 = 4 And, Largest side = 5 Now, 4 < 5 This does not satisfy triangle inequality ∴ Triangle does not exist

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