Math, Gr 10
posted by Anne on .
A rectangular field is to be enclose by 800 meters of fencing and the fourth side with be along the side of a barn.
A) What dimensions will give the maximum area?
B) What is the maximum area?

let the single side by y
let the two other sides be x each
so 2x+y = 800
y = 8002x
area = xy
= x(8002x)
= 2x^2 + 800x
Since you rated this grade 10 , I will assume you don't have Calculus, so let's complete the square
area = 2(x^2  400x <>+4000040000)
= 2( (x200)^2  40000)
= 2(x200)^2 + 80000
the max area is 80,000 m^2 and is obtained when
x = 200 m, which makes y = 8002(200) = 400 m