Question

The construction of a triangle $ABC$, given that $BC=6cm,\angle B=45°$ is not possible when difference of $AB$ and $AC$ is equal to:

• A. $6.9cm$
• B. $5.2cm$
• C. $5.0cm$
• D. $4.0cm$

Answer 1

The correct option is A

$6.9cm$

Step 1: GIven data

As per the data given in the question,

We have,

$BC=6cm,\angle B=45°$

We have to find the possible value of length of difference of $AB$ and $AC$, for constructing the triangle $ABC$

Step 2:

We know that,

For constructing a triangle,

The sum of two sides should less than or equal to third side,

So,

$$\begin{gathered} AB+BC<AC \\ \Rightarrow AB+6<AC \\ \Rightarrow 6<AC–AB \\ \Rightarrow AC–AB>6 \end{gathered}$$

Therefore, when the difference between $AB$ and $AC$ is $6.9cm$, then the construction of a triangle is not possible, cause $6.9cm>6cm$

Thus option (a) is the correct choice.