A rectangular paper, when folded into two congruent parts had a perimeter of 34 cm for each part folded along one set of sides and the same is 38 cm when folded along the other set of sides. What is the area of the paper ?

When folded along breadth, we have :
$$\eqalign{ & 2\left( {\frac{l}{2} \times b} \right) = 34 \cr & or,l + 2b = 34.....(i) \cr} $$
When folded along length, we have :
$$\eqalign{ & 2\left( {l \times \frac{b}{2}} \right) = 38 \cr & or,2l + b = 38.....(ii) \cr} $$
Solving (i) and (ii), we get :
$$l$$ = 14 and b = 10
∴ Area of the paper :
= (14 × 10) cm²
= 140 cm²