Question

The construction of a triangle ABC in which AB = 4 cm, $\angle$A = 60${}^{\circ }$ 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

The correct option is B 4.5 cm

Given, BC = 4 cm 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.,

$\Rightarrow AB+BC>AC$

$\Rightarrow BC>AC–AB$

$\Rightarrow 4>AC–AB$

So, if $AC–AB$ will greater than 4 cm, then construction of $\Delta$ABC is not possible.

So out of the given options only 4.5 cm is greater than 4 cm. Thus, 4.5 cm is the correct answer.