The length of the rectangle is 2 cm more than its width, if the length is increased by 2 cm and the width is reduced by 4 cm

The length of the rectangle is 2 cm more than its width, if the length is increased by 2 cm and the width is reduced by 4 cm, then the area of the rectangle will decrease by 40 cm2 find the original length and width.

Let the initial width of the rectangle be x cm, then the initial length of the rectangle is (x + 2) cm. The initial area of ​​the rectangle is equal to the product of its sides, i.e. x (x + 2) cm ^ 2. If we increase the length by 2 cm, then it will become equal to (x + 2) + 2 = x + 4 cm. If the width of the rectangle is reduced by 4 cm, then it will become equal to (x – 4) cm. After that, the area will become equal to (x + 4) (x – 4) cm ^ 2. By the condition of the problem, it is known that after this the area of ​​the rectangle will decrease by (x (x + 2) – (x + 4) (x – 4)) cm ^ 2 or by 40 cm ^ 2. Let’s make an equation and solve it.
x (x + 2) – (x + 4) (x – 4) = 40;
x ^ 2 + 2x – (x ^ 2 – 16) = 40;
x ^ 2 + 2x – x ^ 2 + 16 = 40;
2x + 16 = 40;
2x = 40 – 16;
2x = 24;
x = 24: 2;
x = 12 (cm) – width;
x + 2 = 12 + 2 = 14 (cm) – length.
Answer. 12 cm, 14 cm.