Question

Question 3
The construction of a $\Delta ABC,$ given that BC = 3cm, $\angle C={60}^{\circ }$ is possible when difference of AB and AC is equal to

(A) 3.2 cm
(B) 3.1 cm
(C) 3 cm
(D) 2.8 cm

Answer 1

(D) 2.8 cm

​​​​​​​Given, BC = 3cm and $\angle C={60}^{\circ }$
We know that, the construction of a triangle is possible, if sum of two sides is greater than the thirde side of the triangle i.e.,
$AB+BC>AC$
$\Rightarrow BC>AC-AB$
$\Rightarrow 3>AC-AB$
So, if AC – AB = 2.8cm, then construction of $\Delta ABC$ with given conditions is possible.