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
mimi
Jun 15, 2017

18 yards, 18 yards, 40 yards

Explanation:

Sorry for this awful quality. Hope this helps though.

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Shwetank Mauria
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.

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