The perimeter of the rectangular section is 60 m and the area is 200 m2. Find his side.

let x be one side of the rectangle
y – the other side of the rectangle
perimeter = x + x + y + y = 2 * x + 2 * y = 2 * (x + y)
area = x * y
then
2 * (x + y) = 60
x * y = 200
got the system of equations
solve it and find x and y
1) 2 (x + y) = 60
x + y = 60/2
x + y = 30
x = 30 – y

2) x * y = 200
(30 – y) * y = 200
– y squared + 30 * y – 200 = 0
Find the discriminant of the quadratic equation:
D = 302 – 4 (-1) (-200) = 900 – 800 = 100
Since the discriminant is greater than zero, the quadratic equation has two real roots:
x1 = (-30 – √1000 / (2 (-1)) = (-30 – 10) / -2 = -40 / -2 = 20
x2 = (-30 + √100) / (2 (-1)) = (-30 + 10) / -2 = -20 / -2 = 10
3) x = 30 – 20 = 10
x = 30 – 10 = 20
answer: one side = 10 cm
other side = 20 cm