Question

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

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

Answer 1

The correct option is A 6.9cm

Given, BC = 6cm and $\angle B={45}^{\circ }$
We know that, the construction of a triangle is not possible, if sum of two sides is less than or equal to the third side of the triangle.
$i.e.,AB+BC\le AC$
$\Rightarrow BC\le AC-AB$
$\Rightarrow 6\le AC-AB$
So, if AC – AB = 6.9cm, then construction of $\Delta ABC$ with given conditions is not possible.