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?

2 Answers
Jun 15, 2017

18 yards, 18 yards, 40 yards

Explanation:

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Jun 15, 2017

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.