Question

If an area is enclosed by the side of a barn using a fence of `76` yards (one side is barn's wall), what is the maximum area that can be covered?

Answer 1

18 yards, 18 yards, 40 yards

Explanation:

Sorry for this awful quality. Hope this helps though.

Answer 2

Maximum area that can be enclosed is `722` square yards.

Explanation:

Let `l` be the length along the side of the barn and `w` be the width.

Hence fencing required will be `l+w+w=l+2w` and this is `76` yards. In other words `l+2w=76` i.e. `w=(76-l)/2=38-l/2`

Area covered by this will be `lxx(38-l/2)=38l-l^2/2`

= `-1/2(l^2-76l)`

= `-1/2(l^2-2xx38xxl+38^2)+1/2xx38^2`

= `-1/2(l-38)^2+722`

It is apparent that as coefficient of `(l-38)^2` is `-1/2`,

`-1/2(l-38)^2` is always negative, except that it is `0` when `l=38` and hence maximum area at this level is `722` square yards and as width is `38-38/2=19`, dimensions would be `38xx19`, with `38` yards along side of the barn.