The width of the rectangle is three times less than its length, if the length of the rectangle is reduced by 2 m

The width of the rectangle is three times less than its length, if the length of the rectangle is reduced by 2 m, then its area will decrease by 8m2, find the original length and width of the rectangle.

Let the width of the rectangle be x meters, then the length of the rectangle is 3 meters (if the width is 3 times less than the length, then the length, on the contrary, is 3 times the width), its area (the area of ​​the rectangle is equal to the product of its sides, S = a * b ) is equal to (x * 3x) m ^ 2. If the length of the rectangle is reduced by 2 meters, then it will become equal to (3x – 2) meters, and its area will become equal to x (3x – 2) m ^ 2. By the condition of the problem, it is known that after decreasing the length, the area of ​​the rectangle will decrease by (x * 3x – x (3x – 2)) m ^ 2 or by 8 m ^ 2. Let’s make an equation and solve it.

x * 3x – x (3x – 2) = 8;

3x ^ 2 – 3x ^ 2 + 2x = 8;

2x = 8;

x = 8: 2;

x = 4 (m) – width;

3x = 3 * 4 = 12 (m) – length.

Answer. 4 m; 12 m.