Question 2 - Figure it out - Page 154 - Chapter 7 Class 7 - A tale of three Intersecting Lines (Ganit Prakash)

Transcript

Question 2 Can we say anything about the existence of a triangle for each of the following sets of lengths? (a) 10 km, 10 km and 25 km (b) 5 mm, 10 mm and 20 mm (c) 12 cm, 20 cm and 40 cm 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) 10 km, 10 km and 25 km Here, Sum of smaller two sides = 10 + 10 = 20 And, Largest side = 25 Now, 20 < 25 This does not satisfy triangle inequality ∴ Triangle does not exist (b) 5 mm, 10 mm and 20 mm Here, Sum of smaller two sides = 5 + 10 = 15 And, Largest side = 20 Now, 15 < 20 This does not satisfy triangle inequality ∴ Triangle does not exist (c) 12 cm, 20 cm and 40 cm Here, Sum of smaller two sides = 12 + 20 = 32 And, Largest side = 40 Now, 32 < 40 This does not satisfy triangle inequality ∴ Triangle does not exist