Increased sides

If side b of the rectangle increases by 1 cm and the other side decreases by 4 cm at the same time, the area of the rectangle decreases by 48 cm². If side b increases by 2 cm and side a decreases by 1 cm at the same time, the area of the rectangle increases by 22 cm². Determine the sides a and b of the rectangle.

Correct answer:

a =  16 cm
b =  20 cm

Step-by-step explanation:

$$\begin{gathered} (a+1)\cdot (b-4)=a\cdot b-48 \\ (a+2)\cdot (b-1)=a\cdot b+22 \\ 4a-b=44 \\ a-2b=-24 \\ Row2-\frac{1}{4}\cdot Row1\to Row2 \\ 4a-b=44 \\ -1.75b=-35 \\ b=\frac{-35}{-1.75}=20 \\ a=\frac{44+b}{4}=\frac{44+20}{4}=16=16\text{cm} \\ a=16 \\ b=20 \end{gathered}$$

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