Question

Can a $\Delta ABC$ can be constructed in which $\angle B={105}^{\circ },\angle C={90}^{\circ }$ and AB + BC + CA = 10cm.

• A. Yes
• B. No
• C. Cannot be determined
• D. Data insufficient

Answer 1

The correct option is B No

Here, $\angle B={105}^{\circ },\angle C={90}^{\circ }$
And $AB+BC+CA=10cm$

We know that, sum of angles of a triangle is ${180}^{\circ }$.
$\therefore \angle A+\angle B+\angle C={180}^{\circ }$
Here,
$\Rightarrow \angle B+\angle C={105}^{\circ }+{90}^{\circ }$$={195}^{\circ }>{180}^{\circ },$ which is not possible in case of triangle.

Thus, $\Delta ABC$ with given conditions cannot be constructed.