Question

Is it possible to draw a triangle, the lengths of whose sides are given below?

(i) 1 cm, 1 cm, 1 cm
(ii) 2 cm, 3 cm, 4 cm
(iii) 7 cm, 8 cm, 15 cm
(iv) 3.4 cm, 2.1 cm, 5.3 cm
(v) 6 cm, 7 cm, 14 cm

Answer 1

(i) Consider numbers 1, 1 and 1.
Clearly, 1 + 1 $>$1
1 + 1 $>$1
1 + 1 $>$1

Thus, the sum of any two sides is greater than the third side.
Hence, it is possible to draw a triangle having sides 1 cm, 1 cm and 1 cm.

(ii)
Clearly, 2 + 3 $>$4
3 + 4 $>$2
2+ 4 $>$3
Thus, the sum of any two sides is greater than the third side.
Hence, it is possible to a draw triangle having sides 2 cm, 3 cm and 4 cm.

(iii)
Clearly, 7 + 8 = 15

Thus, the sum of these two numbers is not greater than the third number.
Hence, it is not possible to draw a triangle having sides 7 cm, 8 cm and 15 cm.

(iv) Consider the numbers 3.4, 2.1 and 5.3.

Clearly: 3.4 + 2.1 $>$5.3
5.3 + 2.1 $>$ 3.4
5.3 + 3.4 $>$ 2.1

Thus, the sum of any two sides is greater than the third side.
Hence, it is possible to draw a triangle having sides 3.4 cm, 2.1 cm and 5.3 cm.

(v) Consider the numbers 6, 7 and 14.
Clearly, 6+7 $\ngtr$ 14

Thus, the sum of these two numbers is not greater than the third number.
Hence, it is not possible to draw a triangle having sides 6 cm, 7 cm and 14 cm.