Question

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

• A. 3.2 cm
• B. 3.1 cm
• C. 3 cm
• D. 2.8 cm

Answer 1

The correct option is 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 third 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.