In each of the following, there are three positive numbers. State if these numbers could possibly be the lengths of the sides of a triangle:
(i) 5, 7, 9
(ii) 2, 10, 15
(iii) 3, 4, 5

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Solution

(i) Given 5, 7, 9
Yes, these numbers can be the lengths of the sides of a triangle because the sum of any two sides of a triangle is always greater than the third side.
Here, 5 + 7 > 9, 5 + 9 > 7, 9 + 7 > 5
(ii) Given 2, 10, 15
No, these numbers cannot be the lengths of the sides of a triangle because the sum of any two sides of a triangle is always greater than the third side, which is not true in this case.
Here, 2 + 10 < 15
(iii) Given 3, 4, 5
Yes, these numbers can be the lengths of the sides of a triangle because the sum of any two sides of triangle is always greater than the third side.
Here, 3 + 4 > 5, 3 + 5 > 4, 4 + 5 > 3

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Q. In each of the following, there are three positive numbers. State if these numbers could possibly be the lengths of the sides of a triangle:
(i) 5, 7, 9
(ii) 2, 10, 15
(iii) 3, 4, 5
(iv) 2, 5, 7
(v) 5, 8, 20

Verify commutativity of addition of rational numbers for each of the following pairs of rational numbers: (i) $\frac{- 11}{5} a n d \frac{4}{7}$ (ii) $\frac{4}{9} a n d \frac{7}{- 12}$ (iii) $\frac{- 3}{5} a n d \frac{- 2}{- 15}$ (iv) $\frac{2}{- 7} a n d \frac{12}{- 35}$ (v) $4 a n d \frac{- 3}{5}$ (vi) $- 4 a n d \frac{4}{- 7}$