Question

Question 5
Write True or False and give reasons for your answer:

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

Answer 1

False

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.