The perimeter of the rectangle is 20 cm. Find its sides if you know that the area of the rectangle is 24 cm2.

Let’s take one side of the rectangle as a and the other as b.
1) compose two equations according to the condition:
1.P = (a + b) 2 = 20,
2. S = a b = 24;
2) express a from the first equation through b and substitute it into the second equation:
(a + b) 2 = 20,
a + b = 20: 2
a + b = 10,
a = 10 – b;
a b = 24,
(10 – b) b = 24,
-b ^ 2 + 10 – 24 = 0,
D = 10 ^ 2 – 4 (-1) (-24) = 100 – 96 = 4,
b1 = (-10 + v4) / 2 (-1) = (-10 + 2) / (- 2) = -8 / -2 = 4 cm,
b2 = (-10 – v4) 2 (-1) = -12 / -2 = 6 cm;
3) calculate the value of a:
a = 10 – b,
a1 = 10 – 4 = 6 cm,
a2 = 10 – 6 = 4 cm.
Answer: if a = 6 cm, then b = 4 cm; if a = 4 cm, then b = 6 cm.