If two sides of a triangle are of lengths 5 cm
Question:

If two sides of a triangle are of lengths 5 cm and 1.5 cm, then the length of third side of the triangle cannot be

(a) 3.6 cm

(b) 4.1 cm

(c) 3.8 cm

(d) 3.4 cm

Thinking Process

Use the condition that, sum of any two sides of a triangle is greater than third side and difference of any two sides is less than the third side.

Solution:

(d) Given, the length of two sides of a triangle are 5 cm and 1.5 cm, respectively.

Let sides AB = 5 cm and CA = 1.5 cm

We know that, a closed figure formed by three intersecting lines (or sides) is called a triangle, if difference of two sides < third side and sum of two

sides > third side

∴ 5-1.5 < BC and 5+1.5 > BC

=> 3.5 < BC and 6.5 > BC

Here, we see that options (a), (b) and (c) satisfy the above inequality but option (d) does not satisfy the above inequality.