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 = 800-2x
area = xy
= -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 <>+40000-40000)
= -2( (x-200)^2 - 40000)
= -2(x-200)^2 + 80000
the max area is 80,000 m^2 and is obtained when
x = 200 m, which makes y = 800-2(200) = 400 m