The length of a rectangular piece of land is 4 times its width. If the length of this plot is increased by 2m

The length of a rectangular piece of land is 4 times its width. If the length of this plot is increased by 2m, and the width is reduced by 5 meters, then its area will decrease by 190 m2. what are the dimensions of this site.

Let the width of the rectangular section be x, then the length, which is 4 times greater, is 4x.

The area of ​​this rectangle will be equal to:

4x * x = 4x ^ 2 (m2).

With an increase in length by 2 m, it will be equal to (4x + 2) m, and with a decrease in width by 5 m, it will

will be (x – 5) m.

Then the new area will be equal to:

(x – 5) * (4x + 2) = 4x ^ 2 – 20x + 2x -10 = 4×2 – 18x – 10.

By condition, the new area will be 190 m2 less than the primary one.

You can compose an expression:

4x ^ 2 – (4x ^ 2 – 18x – 10) = 190.

Expand the brackets:

4x ^ 2 – 4x ^ 2 + 18x + 10 = 190.

We leave the unknowns on the left side, the known ones we transfer to the right with the opposite sign:

18x = 190 – 10;

18x = 180;

x = 180: 18;

x = 10 (m) – the width of the site.

4x = 4 * 10 = 40 (m) – the length of the section.

Answer: the width of this section is 10 m, and the length is 40 m.