Question

The construction of a triangle ABC in which AB = 4 cm, ∠A = 60° is not possible when difference of BC and AC is equal to
(a) 3.5 cm
(b) 4.5 cm
(c) 3 cm
(d) 2.5 cm

Answer 1

We know,
In a triangle, sum of any two sides must be greater than the third side.

$$\begin{gathered} AB+AC>BC \\ \Rightarrow AB>BC-AC \\ \Rightarrow 4>BC-AC\left(\because AB=4\mathrm{cm}\right) \\ \Rightarrow 4>BC-AC \end{gathered}$$

Thus, difference of BC and AC cannot be greater than 4 cm.
​
Hence, the correct option is (b).