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 10 + 15.

Question

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  10 + 15.

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Do it yourself.
NCERT In-Text Questions (Page 154)
Will this always happen? That is, for any set of lengths, will there be at least two comparisons where the direct length is less than the sum of the other two? Explore different sets of lengths.
Solution:
(i) 5 mm, 10 mm, 20 mm.
There are two comparisons where this happens:
10  10 + 5
(ii) 12 cm, 20 cm and 40 cm.
There are two comparisons where this happens:
12  12 + 20
Further, for a given set of lengths, is it possible to identify which lengths will immediately be less than the sum of the other two, without calculations?
[Hint: Consider the direct lengths in the increasing order]
Solution:
Yes, it is possible to identify which lengths will immediately be less than the sum of the other two, if we take the direct lengths in increasing order.
Figure it Out (Page 156)

A Tale of Three Intersecting Lines — Question 3