Question

A rectangular field has perimeter 600 m and area 21600 m squared. Find the dimensions of the field.​

Answer 1

Let length be x and width be y

`perimeter = 2(l + w) \\ 600 = 2(x + y) \\ x + y = 300 - - - (a) \\ \\ area = l * w \\ 21600 = xy - - - (b) \\ from \: (a) : \\ y = 300 - x \\ \therefore21600 = x(300 - x) \\ 21600 = 300x - {x}^(2) \\ {x}^(2) - 300x + 21600 = 0 \\ (x - 180)(x - 120) = 0 \\ x = 180 \: \: or \: \: 120 \: m \\ \\ y = 120 \: \: or \: \: 180 \: m \\ \\ { \boxed{ length = 180 \: m}} \\ { \boxed{width = 120 \: m}}`