The length of the rectangle is 20 m longer than its width. if the length of the rectangle is reduced by 10 m, and the width

The length of the rectangle is 20 m longer than its width. if the length of the rectangle is reduced by 10 m, and the width is increased by 6 m, then its area will increase by 12 m2. Find the sides of the rectangle.

Let the width of the rectangle be x meters, then the length of the rectangle is (x + 20) meters, and its area is x (x + 20) m ^ 2. If the length of the rectangle is reduced by 10 m, then it becomes equal to (x + 20) – 10 = x + 10 meters. If the width of the rectangle is increased by 6 m, then it will become equal to (x + 6) m, and the area of ​​the rectangle will be equal to (x + 10) (x + 6) m ^ 2. By the condition of the problem, it is known that the area of ​​the rectangle has become larger than the original area by (x + 10) (x + 6) – x (x + 20) m ^ 2 or by 12 m ^ 2. Let’s make an equation and solve it.

(x + 10) (x + 6) – x (x + 20) = 12;

x ^ 2 + 10x + 6x + 60 – x ^ 2 – 20x = 12;

-4x = 12 – 60;

-4x = -48;

x = -48: (-4);

x = 12 (m) – width;

x + 20 = 12 + 20 = 32 (m) – length

Answer. 12 m; 32 m.