The length of the rectangle was increased by 1 m, and the width was decreased by 1 mm

The length of the rectangle was increased by 1 m, and the width was decreased by 1 mm. Could the area of the rectangle decrease in this case?

Suppose the length of the rectangle is A and the width of the rectangle is B.

Area S of the rectangle:

S = A * B.

If the length is increased by 1, then the length will be equal to A + 1,

and if we decrease the width by 1, then it becomes B – 1.

The area S1 of this rectangle:

S1 = (A + 1) * (B – 1).

Suppose S> S1. Then:

A * B> (A + 1) * (B – 1) = A * B – A + B – 1,

0> – A + B – 1,

A + 1> B.

Thus, we got that if the length of the rectangle increased by 1 mm is greater than the width, then the area of the rectangle will decrease.