Question

Can we construct a $∆ABC$ where $AB=5cm$, $\angle A=45°$ and $(BC+AC)=5cm$ ? Justify.

Answer 1

State that whether the construction of a triangle is possible or not

It is known that the construction of a triangle can only be possible if the sum of two sides is greater than the third side.

It is given that $AB=5cm$.

So, the sum of the other two sides will be greater than $AB$.

Thus,

$$\begin{gathered} BC+AC>AB \\ \Rightarrow BC+AC>5cm \end{gathered}$$

Thus, if $(BC+AC)=5cm$ then the construction of the triangle is not possible.

Hence, the construction of a triangle is not possible.