The rectangle is 8cm longer than the width. After that, the length was increased by 5 cm, and the width was decreased by 4 cm

The rectangle is 8cm longer than the width. After that, the length was increased by 5 cm, and the width was decreased by 4 cm, its area decreased by 40 cm2. Find the sides of the given rectangle.

Let’s say the length of the first rectangle is x cm.

Since it is 8 cm larger than the width, its value was: x – 8 cm.

So the area of the first rectangle was equal to:

x * (x – 8) = x ^ 2 – 8 * x.

After the length was increased, it was: x + 5 cm.

The width became equal: x – 8 – 4 = x – 12 cm.

So the new area was:

(x + 5) * (x – 12) = x ^ 2 – 12 * x + 5 * x – 60 = x ^ 2 – 7 * x – 60.

The area difference was:

(x ^ 2 – 8 * x) – (x ^ 2 – 7 * x – 60) = 40.

x ^ 2 – 8 * x – x ^ 2 + 7 * x + 60 = 40.

-x = -20.

x = 20 (initial length).

x – 8 = 20 – 8 = 12 cm (initial width).

Answer: 20 and 12 cm.