The perimeter of the rectangle is 6 cm. Find the lengths of its sides if the base is 1.8 times the height.

Let us denote by a – the height of the rectangle, b – the base of the rectangle.
Then from the condition you can make the equation: 1.8a = b.
As you know, the perimeter of a rectangle is calculated by the formula: P = (a + b) * 2, where a is the height of the rectangle, b is the base of the rectangle.
Substitute all known values into the formula and calculate the height of the rectangle: 6 = (a + 1.8a) * 2.
6 = 2.8a * 2 = 5.6a.
a = 6 / 5.6 = 1.07 cm.
b = 1.8 * 1.07 = 1.926 cm.
Answer: The height of the rectangle is 1.07 cm, the base of the rectangle is 1.926 cm.