Question

Question 2
The construction of $\Delta ABC$, given that BC = 6cm, $\angle B={45}^{\circ }$ 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

(A) 6.9 cm

Given, BC = 6cm and $\angle B={45}^{\circ }$
We know that, when the sum of any two sides of a triangle is greater than the third side only then the construction of that particular triangle is possible.
Now lets take any pair of sides,
$i.e.,AC+BC>AB$
$\Rightarrow BC>AB-AC$
$\Rightarrow 6>AB-AC$
So, if AB – AC = 6.9cm, then construction of $\Delta ABC$ with given conditions will not possible.