The rectangular lawn is surrounded by a 40m long fence. Lawn area 96m ^ 2. Find the lengths of the sides of the lawn.

The fence is 40 meters long – this is the perimeter of the rectangle. Lawn area – 96m ^ 2 – rectangle area.
Perimeter = 2a + 2b = 40
Area = a * b = 96
Let’s compose a system of equations:
2a + 2b = 40, a * b = 96
Let us express a from the first equation: a = 20-b
Let’s substitute this expression three times: (20-b) * b = 96
20b-b ^ 2-96 = 0
Let’s solve the quadratic equation and get the roots: b = 12 and b = 8
Let’s find a with these values: b = 12, a = 8 or b = 8, a = 12
Answer: 8m and 12m