Question

The construction of a triangle ABC, given that BC = 3 cm, ∠C = 60° is possible when differences of AB and AC is equal to
(a) 3.2 cm
(b) 3.1 cm
(c) 3 cm
(d) 2.8 cm

Answer 1

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

$$\begin{gathered} AB+BC>AC \\ \Rightarrow BC>AC-AB \\ \Rightarrow 3>AC-AB\left(\because BC=3\mathrm{cm}\right) \\ \Rightarrow 3>AC-AB \end{gathered}$$

Thus, differences of AB and AC can be 2.8 cm.

Hence, the correct option is (d).