Question

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

Answer 1

(i) 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) 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.

(iii) 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,
$3+4>5,3+5>4,4+5>3$

(iv) 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,
$2+5=7$

(v) 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,
$5+8<20$