a rectangular field has a perimeter of 500m and an area of 14400m2. Find the lengths of the sides

Perimeter = 500 = 2x + 2y, where x and y are the length and width

area = 14400 = xy

x = 14400 / y

substitute:

500 = (2 * (14400/y)) + 2y

[multiply by y]

500y = 28800 + 2y^2

2y^2 - 500y + 28800 = 0

y^2 - 250y + 14400 = 0

use the quadratic equation: y = (-b ± (b^2 - 4*a*c) ^1/2) / 2a

the answers should be written in the form (y - answer one) (y - answer two)

substitute these answers into x = 14400 / y to find x

remember x and y can not be negative as they are lengths