Question

The construction of a triangle ABC, given BC = 6 cm, ∠B = 45° is not possible when difference of AB and AC is equal to
(a) 6.9 cm
(b) 5.2 cm
(c) 5 cm
(d) 4 cm

Answer 1

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

$$\begin{gathered} AB+BC>AC \\ \Rightarrow BC>AC-AB \\ \Rightarrow 6>AC-AB\left(\because BC=6\mathrm{cm}\right) \\ \Rightarrow 6>AC-AB \end{gathered}$$

Thus, difference of AB and AC cannot be greater than 6 cm.
​
Hence, the correct option is (a).