Question 3 - Figure it out - Page 154 - Chapter 7 Class 7 - A tale of three Intersecting Lines (Ganit Prakash)

Transcript

Question 3 For each set of lengths seen so far, you might have noticed that in at least two of the comparisons, the direct length was less than the sum of the other two (if not, check again!). For example, for the set of lengths 10 cm, 15 cm and 30 cm, there are two comparisons where this happens: 10 < 15 + 30 15 < 10 + 30 But this doesn’t happen for the third length: 30 > 10 + 15. We need to check Triangle Inequality for 10, 15, 30 Triangle Inequality says Sum of Two Sides > Third Side So, we have these options 10 + 30 > 15 40 > 15 This is true Then, we try 15 + 30 > 10 45 > 10 This is true And, lastly 10 + 15 > 30 25 > 30 This is not true Now, to check triangle inequality either we can check all possible cases Or, we can compare the largest side We can just check Sum of smaller sides > Largest side Thus, If true, all other cases would be true If false, then triangle inequality is not satisfied