Question

In which of the following cases, a unique triangle can be drawn?

• A. $AB=4cm,BC=8cm$ and $CA=2cm$
• B. $BC=5.2cm,\angle B={90}^o$ and $\angle C={110}^o$
• C. $XY=5cm,\angle X={45}^o$ and $\angle Y={60}^o$
• D. An isosceles triangle with the length of each equal side $6.2cm$.

Answer 1

The correct option is C $XY=5cm,\angle X={45}^o$ and $\angle Y={60}^o$

A triangle Is possible if
(i) Sum of any two sides must be greater than the third side.
(ii) Sum of all angles must be equal to ${180}^o$180o.

So, in options (A) and (B) triangle are not possible because of above points (i) and (ii) respectively.

In option (D) we can draw more than one isosceles triangle with side length $6.2$ cm.

So, triangle is not unique.

Hence, only in option (C), a unique triangle can be drawn.