The sides of the rectangle are proportional to the numbers 3: 4, and its area is 48 cm.

The sides of the rectangle are proportional to the numbers 3: 4, and its area is 48 cm. Determine the area of the circle circumscribed about the rectangle.

We denote by x one third of the smaller of the sides of the given rectangular quadrangle.

Then the smaller side of this rectangle should be equal to 3 cm.

Since the sides of this rectangle are 3: 4, the large side of this rectangle should be 4x cm.

According to the condition of the problem, the area of ​​this rectangle is 48 cm ^ 2, therefore, we can draw up the following equation:

3x * 4x = 48,

solving which, we get:

12x ^ 2 = 48;

x ^ 2 = 48/12;

x ^ 2 = 4;

x = 2 cm.

Find the length of the diagonal of the given rectangle;

√ ((3x) ^ 2 + (4x) ^ 2) = √ (9x ^ 2 + 16x ^ 2) = √ (25x ^ 2) = 5x = 5 * 2 = 10 cm.

Since the diameter of the circle circumscribed around the rectangle is equal to the diagonal of this rectangle, the radius of the circle circumscribed around this rectangle is 2/1 = 1 cm, and the area of ​​this circle is n * 1 ^ 2 = n cm ^ 2.

Answer: n cm ^ 2.