Question

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

• A. True
• B. False

Answer 1

The correct option is B

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${}^{\circ }$​.

Here,$\angle$A + $\angle$B + $\angle$C = 180${}^{\circ }$

$\angle$B + $\angle$C = 105${}^{\circ }$ + 80${}^{\circ }$ = 185${}^{\circ }$, which is not true.

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