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.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.