Find the sides of a rectangle whose area is 24 cm2 and the perimeter is 20 cm.

Let us designate the length of one of the sides of the rectangle by “x”, and the other by “y”.
The area of the rectangle is xy, by condition it is 24cm2.
The perimeter is 2 (x + y), according to the condition it is 20cm.
You can create a system of equations:
xy = 24,
2 (x + y) = 20;

xy = 24,
x + y = 10;

express x = 10-y and substitute it into the equation xy = 24
(10-y) y = 24;
y ^ 2-10y + 24 = 0;

We solve the quadratic equation.
Discriminant: D = 100-4 * 24 = 100-96 = 4;

y1 = (10 + 2) / 2 = 6;
y2 = (10-2) / 2 = 4;

If y = 6, then x = 10-6 = 4. If y = 4, then x = 10-4 = 6.
This is the same rectangle with sides 4cm and 6cm.

Answer: 4cm and 6cm.