Find the area of a rectangle whose base is twice the height and whose area is numerically equal to the perimeter.

We have a rectangle whose length is twice its width.

At the same time, the rectangle of the wound has the size of the perimeter and area.

The perimeter of the rectangle is twice the sum of the length and width.

The area of a rectangle is the product of length and width.

Let’s introduce a variable:

Let m be the width of the rectangle, then (2 * m) is its length. Let’s compose and solve the equation:

m * 2 * m = 2 * (m + 2 * m);

2 * m ^ 2 = 6 * m;

m ^ 2 = 3 * m.

Obviously, m = 0 (cannot be) and m = 3.

Then the sides of the rectangle are 3 cm and 6 cm long.