Question

In a squared sheet, draw two triangles of equal areas such that

(i) The triangles are congruent.

(ii) The triangles are not congruent.

What can you say about their perimeters?

Answer 1

(i)

Here, ΔABC and ΔPQR have the same area and are congruent to each other also.
So, from the rule of corresponding parts of congruent triangles($CPCT$), we have $AB=PQ$
$BC=QR$ and $CA=PR$
Adding above three expressions, we get
$AB+BC+CA=PQ+QR+PR$
$\Rightarrow$ Perimeter of $ABC=$Perimeter of $PQR$
Hence, the perimeter of both the triangles will be the same.

(ii)

Here, the two triangles have the same height and base. Thus, their areas are equal. However, these triangles are not congruent to each other.
So, their corresponding sides need not be equal, which implies, the perimeter of both the triangles will not be the same.