Question

The lengths of three segments are given for constructing a triangle. Say whether a triangle with these sides can be drawn. Give the reason for your answer.
(1) 17 cm, 7 cm, 8 cm (2) 7 cm, 24 cm, 25 cm
(3) 9 cm, 6 cm, 16 cm (4) 8.4 cm, 16.4 cm, 4.9 cm
(5) 15 cm, 20 cm, 25 cm (6) 12 cm, 12 cm, 16 cm

Answer 1

(1) 17 cm, 7 cm, 8 cm
Here, 17 > 7 + 8 or 17 > 15
In any triangle, the sum of the lengths of any two sides of a triangle is always greater than the third side.
Therefore, the traingle is not possible.
(2) 7 cm, 24 cm, 25 cm
Here, 7 < 24 + 25 or 7 < 49
24 < 7 + 25 or 24 < 32
25 < 7 + 24 or 25 < 31
In any triangle, the sum of the lengths of any two sides of a triangle is always greater than the third side.
Therefore, the traingle is possible.
(3) 9 cm, 6 cm, 16 cm
Here, 16 > 9 + 6 or 16 > 15
In any triangle, the sum of the lengths of any two sides of a triangle is always greater than the third side.
Therefore, the traingle is not possible.
(4) 8.4 cm, 16.4 cm, 4.9 cm
Here, 16.4 > 8.4 + 4.9 or 16.4 > 13.3
In any triangle, the sum of the lengths of any two sides of a triangle is always greater than the third side.
Therefore, the traingle is not possible.
(5) 15 cm, 20 cm, 25 cm
Here, 15 < 20 + 25 or 15 < 45
20 < 15 + 25 or 20 < 40
25 < 15 + 20 or 25 < 35
In any triangle, the sum of the lengths of any two sides of a triangle is always greater than the third side.
Therefore, the traingle is possible.
(6) 12 cm, 12 cm, 16 cm
Here, 12 < 12 + 16 or 12 < 28
12 < 12 + 16 or 12 < 28
16 < 12 + 12 or 16 < 24
In any triangle, the sum of the lengths of any two sides of a triangle is always greater than the third side.
Therefore, the traingle is possible.