The lengths of the sides of the rectangle are proportional to the numbers 7 and 3.

The lengths of the sides of the rectangle are proportional to the numbers 7 and 3. find the area of the rectangle if the perimeter is 120 cm.

The perimeter of a rectangle whose opposite sides are equal is calculated by the formula:

P = 2a + 2b.

According to the condition of the assignment, we will compose an equation for this formula if P = 120 cm, and the sides are proportional to the numbers 7 and 3:

2 * 7x + 2 * 3x = 120.

Let’s perform actions with the coefficients of the variable on the left side of the equation:

14x + 6x = 120.

20x = 120.

The second factor is the quotient of the first one:

x = 120: 20 = 6.

Therefore, length = 7 * 6 = 42 cm, width = 3 * 6 = 18 cm.

Let’s find the area by the formula:

S = a * b = 42 * 18 = 756 cm².