Question

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

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

Answer 1

Answer: (A)

$6.9$ cm

According to the theorem of inequalities, the sum of any two sides of the triangle is greater than the third side.

Therefore, $AC+BC>AB$

$\Rightarrow BC>AB-AC$

Therefore, only the first option that is $6.9$ cm does not satisfy the above equation. Rest all the options satisfy the equation.