Find the area of a rectangle if its perimeter is 100 and the ratio of adjacent sides is exactly 1: 4.

Let’s find the lengths of the sides of this rectangle.

Let’s denote by x the width of this rectangle.

In the problem statement, it is said that the lengths of the adjacent sides of a given rectangle are 1: 4.

Therefore, the length of this rectangle is 4 times its width and is 4x.

According to the condition of the problem, the perimeter of this rectangle is 100, therefore, we can make the following equation:

2 * (4x + x) = 100.

We solve the resulting equation:

2 * 5x = 100;

10x = 100;

x = 100/10;

x = 10.

Let’s find the length of this rectangle:

4x = 4 * 10 = 40.

Let’s find the area of ​​this rectangle:

40 * 10 = 400.

Answer: The area of ​​this rectangle is 400.