Posted by **Anne** on Monday, May 6, 2013 at 8:53pm.

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?

- Math, Gr 10 -
**Reiny**, Monday, May 6, 2013 at 10:09pm
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 <>+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

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