Find the sides of a rectangle, knowing that the aspect ratio is 5: 4 and the area is 500 cm2.

Let’s denote the sides of the rectangle by x and y.
According to the condition of the problem, the aspect ratio of this rectangle is 5: 4, therefore, the following ratio is true:
x / y = 5/4.
It is also known that the area of ​​this rectangle is 500 cm2, therefore, the following relationship is true:
x * y = 500.
We solve the resulting system of equations. Substituting into the second equation the value x = (5/4) * y from the first equation, we get:
(5/4) * y * y = 500.
We solve the resulting equation:
(5/4) * y ^ 2 = 500;
y ^ 2 = 500 / (5/4);
y ^ 2 = 500 * (4/5);
y ^ 2 = 400;
y ^ 2 = 20 ^ 2;
y = 20.
Knowing y, we find x:
x = (5/4) * y = (5/4) * 20 = 25.
Answer: the sides of this rectangle are 25 cm and 20 cm.