A rectangle is 8 cm longer than wide. After the length was increased by 5 cm and the width was decreased by 4 cm

A rectangle is 8 cm longer than wide. After 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 this rectangle.

Let the sides of the rectangle be A (length) and B (width).
Then, by the problem statement:
A = B + 8.
Then the area S of the rectangle:
S = A * B = (B + 8) * B.
After the length was increased by 5 cm and the width was decreased by 4 cm, its area S1 decreased by 40 cm ^ 2.
Hence,
S1 = (A + 5) * (B – 4) = S – 40,
A * B – 4 * A + 5 * B – 20 = A * B – 40,
20 = 4 * A – 5 * B = 4 * (B + 8) – 5 * B = 32 – B,
B = 12,
A = B + 8 = 20.