The length of the rectangular piece of land adjacent to the swamp is 80 meters more wide. After drainage works

The length of the rectangular piece of land adjacent to the swamp is 80 meters more wide. After drainage works, the length and width were increased each by 30 meters. And then the length of the plot turned out to be twice the width. How much did the area increase?

Let’s denote by x the length of the original rectangular piece of land.

According to the condition of the problem, the length of the section was 80 m greater than its width, therefore, the width of this section was x – 80 m.

According to the condition of the problem, after drainage works, the length and width of the section were increased each by 30 m, and then the length of the section turned out to be twice the width, therefore, we can draw up the following equation:

x + 30 = 2 * (x – 80 + 30).

We solve the resulting equation:

x + 30 = 2 * (x – 50);

x + 30 = 2x – 100;

2x – x = 30 + 100;

x = 130.

We find the area of ​​the original site:

130 * (130 – 30) = 130 * 100 = 13000 m ^ 2.

We find the area of ​​the site after drainage:

(130 + 30) * (100 + 30) = 160 * 130 = 20800 m ^ 2.

We find how much the area of ​​the site was increased:

20800 – 13000 = 7800 m ^ 2.

Answer: the area of ​​the site was increased by 7800 m ^ 2.