The width of the rectangle is 2 times less than its length, if the width is increased by 10, and the length is reduced by 12

The width of the rectangle is 2 times less than its length, if the width is increased by 10, and the length is reduced by 12, but you will get rectangles with equal areas, find the dimensions of the original rectangle.

Let’s say that the width of the rectangle is x, then its length is 2 * x.

If the width is increased by 10, then it will be x + 10, and if the length is reduced by 12, then it will be equal to 2 * x – 12.

Thus, according to the condition of the problem, we can compose the following equation:

2 * x * x = (x + 10) * (2 * x – 12),

2 * x² = 2 * (x + 10) * (x – 6),

x² = x² – 6 * x + 10 * x – 60,

4 * x – 60 = 0,

4 * x = 60,

x = 60: 4,

x = 15 – the width of the rectangle,

15 * 2 = 30 – the length of the rectangle.