# The area of the rectangle is 48 square centimeters, and its sides are 1: 3.

**The area of the rectangle is 48 square centimeters, and its sides are 1: 3. Find the area of a square that has the same perimeter as a rectangle.**

According to the condition of the assignment, we will compose an equation and find the sides of a rectangle related to 1: 3, the area of which is 48 cm² /

S = a * b. Consequently:

x * 3x = 48.

On the left side of the equation, we perform actions with the coefficients of the variable:

3x² = 48.

The second factor is the quotient of the first one.

x² = 48: 3 = 16.

x = √16 = 4.

Width = 4 cm, length = 3 * 4 = 12 cm.

The perimeter corresponds to the formula:

P = 2a + 2b = 2 * 12 + 2 * 4 = 24 + 8 = 32 cm.

The square has the sum of all sides = 32 cm, calculated by the formula: P = 4a.

Let’s express the side:

a = P: 4 = 32: 4 = 8 cm.

Since all sides of it are equal, the area is:

S = a² = 8 * 8 = 64 cm².