Find the area of a rectangle with a perimeter of 90 cm if the aspect ratio is 4: 5.

If the sides are 4: 5, then one side is 4x and the other is 5x.

The perimeter is equal to the sum of the lengths of all sides of the rectangle, but since the parallel sides are pairwise equal, then P = (a + b) * 2.

Let’s make the equation:

(4x + 5x) * 2 = 90;

9x * 2 = 90;

9x = 45;

x = 5;

One side is 5 * 4 = 20 cm, the other side is 5 * 5 = 25 cm;

We find the area by the formula: S = a * b;

S = 20 * 25 = 500 cm ^ 2.

Answer: 500 cm ^ 2.