Question

In a squared sheet, draw two triangles of equal areas such that
(i) the triangles are congruent.
(ii) the triangles are not congruent.
Will their perimeters be the same?

• A. True
• B. False

Answer 1

The correct option is A True

Two congruent triangles

Here, $\Delta ABC\cong \Delta DEF$

$\therefore ar\left(ABC\right)=2+2=4$ sq. units

$ar\left(DEF\right)=2+2=4$ sq. units

$\therefore ar\left(ABC\right)=ar\left(DEF\right)$

Thus, triangles are of equal areas and are congruent

Now,

To check perimeter of both triangles,

As $\Delta ABC\cong \Delta DEF$

By CPCT

$AB=DE$

$BC=EF$

$AC=DF$

$\therefore$ By adding,

$AB+BC+AC=DE+EF+DF$

$\therefore$ Perimeter of $\Delta ABC=$Perimeter of $\Delta DEF$

Thus, perimeter of congruent triangles are also equal.