The area of the square is 25 a, and its perimeter is 2 times less than the perimeter of the rectangle.

The area of the square is 25 a, and its perimeter is 2 times less than the perimeter of the rectangle. The rectangle is 40 m longer than the width. Find the area of the rectangle.

Given: S square = 25 a; P of the square is 2 times less than the perimeter of the rectangle; The length of the rectangle is 40 m longer than its width.
Find: S rectangle.
The area of ​​the square is 25 a. In fact, since all sides of a square are equal, the formula for its Area is: S = a ^ 2. Knowing this, we can find the side of the square:
S = a ^ 2; 25 = a ^ 2; a = 5 (ap).
The perimeter of a square is the sum of all its sides, or the side multiplied by 4:
P = 5 + 5 + 5 + 5 = 20 (ar).
Or:
P = 4 * 5 = 20 (ar).
The condition says that the perimeter of the square is 2 times less than the perimeter of the rectangle:
20 * 2 = 40 (ar) – the perimeter of the rectangle.
In one area there are 100 m, therefore 40 ar = 40 * 100 = 4000 (meters).
In a rectangle, its length is 40 m longer than its width. Let’s take the width as X m, then the length will be X + 40 m.
The perimeter of a rectangle is the sum of all its sides (or twice the sum of its sides):
X + X + X + 40 + X + 40 = 4000;
4X + 80 = 4000;
4X + 80 – 4000 = 0;
4X – 3920 = 0;
4X = 3920;
X = 3920: 4;
X = 980.
The width of the rectangle is 980 meters.
Then the length is:
980 + 40 = 1020 (meters) – the length of the rectangle.
The area of ​​a rectangle is the product of its two sides:
S = 980 * 1020 = 999600 m ^ 2.
In one area of ​​100 square meters:
999600: 100 = 9996 (ar).
Answer: S = 9996 ar.