Question

The construction of a $∆ABC$ in which $AB=4cm,$ $\angle A=60°$ is not possible when difference of $BC$ and $AC$ is equal to:

• A. $3.5cm$
• B. $4.5cm$
• C. $3cm$
• D. $2.5cm$

Answer 1

The correct option is B

$4.5cm$

Step 1: Given data:

As per the data given in the question,

We have,

$AB=4cm,$ $\angle A=60°$

We have to determine the possible length of difference of $BC$ and $AC$. such that $∆ABC$ can be constructed.

Step 2: Concept related to Triangle

We know that,

The sum of two sides is less than or equal to the third side

So, the construction of triangle can be possible if $AB+BC<AC$

$$\begin{gathered} \Rightarrow 4+BC<AC \\ \Rightarrow 4<AC–BC \end{gathered}$$

Therefore, the construction of a triangle is not possible, when the difference between $BC$ and $AC$ is $4.5cm.$

Therefore, option (b) is correct.