In a squared sheet, draw ΔABC and Δ PQR. When two triangles have equal areas and

(i) these triangles are congruent, i.e., Δ ABC ≅ Δ PQR [By SSS congruence rule]

Then, their perimeters are same because length of sides of first triangle are equal to the length of sides of another triangle by SSS congruence rule.

(ii) But, if the triangles are not congruent, then their perimeters are not same because lengths of sides of first triangle are not equal to the length of corresponding sides of another triangle.