Question

Goutham has been asked to draw a triangle with three lengths given to him. He hasn't checked the given lengths and promised that he will draw the triangle thinking that a triangle can always be constructed with any three lengths. Is it true that a triangle can always be constructed with any three lengths?

• A. True
• B. False

Answer 1

The correct option is B

False

The triangle inequality states that for any triangle, the sum of the lengths of any two of its sides must be greater than or equal to the length of the third side. We, thus, cannot construct a triangle with any three lengths.

Assume a triangle with sides lengths 6, 10, 7 cms. Using the property of triangles, we can see that
(i) 6 + 7 = 13 > 10
(ii) 7 + 10 = 17 > 6
(iii) 10 + 6 = 16 > 7
Hence, it is possible to draw a triangle with these lengths.


Assume a triangle with sides lengths 6, 2, 3 cms. Using the property of triangles, we can see that
(i) 6 + 2 = 8 > 3
(ii) 2 + 3 = 5 < 6
(iii) 3 + 6 = 9 > 7​​​​​​​
Hence, it is not possible to draw a triangle with these lengths since their sides do not meet each other.