Question

The construction of a $∆ABC$, given that$BC=3cm,\angle C=60°$ is possible when difference of $ABandAC$ is equal to:

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

Answer 1

The correct option is D

$2.8cm$

Explanation for correct option : (d)

Step 1: Given data:

As per data given in the question,

We have,

$BC=3cmand\angle C={60}^o$

Step 2: Rules for constructing a triangle:

Since, we know that the sum of two sides of a triangle is greater than the third side.

So,

$$\begin{gathered} AC+BC>AB \\ \Rightarrow AC+3>AB \\ \Rightarrow 3>AB–AC \end{gathered}$$

Therefore, the difference between $ABandAC$ should be less than $3.$

Thus option (d) is correct, cause $2.8<3.$