What are the sides of the rectangle in Figure 55, a cane 3 x width 5x length if its perimeter is 240 cm?

Since the opposite sides in a rectangle are equal to each other, its perimeter can be found by the formula:
P = a + b + a + b = 2 * a + 2 * b,
where P is the perimeter, a is the length, b is the width.
By condition, the perimeter of the rectangle is 240 cm, and the length and width are proportional to the numbers 5 and 3, respectively, then:
2 * 5 * x + 2 * 3 * x = 240.
Let’s solve the resulting linear equation with one variable:
10 * x + 6 * x = 240;
16 * x = 240;
x = 240/16;
x = 15.
Let’s find what the length of the rectangle is:
5 * x = 5 * 15 = 75 (cm).
Find the width of the rectangle:
3 * x = 3 * 15 = 45 (cm).
Answer: the sides of the rectangle are 75 cm (length) and 45 cm (width).