Question

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?

Answer 1

let the single side by y
let the two other sides be x each

so 2x+y = 800
y = 800-2x

area = xy
= x(800-2x)
= -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 <>[phone]</b>)
= -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