7.2. If the width of a rectangle is increased by 3 cm and the height is decreased by 3 cm, its area will not change. How will the area change if, instead, the width of the original rectangle is decreased by 4 cm and the height is increased by 4 cm?
Answer. It will decrease by $28 \mathrm{~cm}^{2}$. Solution. Let the width of the original rectangle be $s$, and the height $h$. The area of the original rectangle is $sh$, and the area of the modified one is $(s+3)(h-3)$, which equals $sh+3(h-s)-9$. Given the equality of areas, $3(h-s)-9=0$, from which $h-s=3$. In the second variation of the change, we get the area $(s-4)(h+4)=sh-4(h-s)-16=sh-4\cdot3-16=sh-28$. Therefore, the area will decrease by $28 \mathrm{~cm}^{2}$.