The lengths of the sides of the rectangle are proportional to the numbers 3 and 5. Find the area of a rectangle if its perimeter is 80 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 task, we will compose an equation for this formula, if P = 80 cm, and the sides are proportional to the numbers 3 and 5:

2 * 5x + 2 * 3x = 80.

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

10x + 6x = 80.

16x = 80.

The second factor is the quotient of the first:

x = 80: 16 = 5.

Therefore, length = 5 * 5 = 25 cm, width = 3 * 5 = 15 cm.

Let’s find the area by the formula:

S = a * b = 25 * 15 = 375 cm².