A farmer has 400 metres of fencing

Question

A farmer has 400 metres of fencing which will be used to enclose a rectangular pasture with an area of 15 000

m^2. Only three sides of the pasture will need fencing as a river will form the boundary of the fourth side.

Determine the possible dimensions of the pasture if all the fencing is to be used.

Answer 1

A = 15,000 m^2

2x +y = 400 m

y = 400-2x

A = XY = x(400-2x) = 400x -2x^2 = 15000

2x^2 -400x +15000 = 0

x^2 -200x + 7500 = 0

(x-50)(x-150) = 0

x =50

y = 300

or x=150 y = 100