You are building a fence on a rectangular lot. Only three sides of the lot will be fenced. You have 15 meters of wood for the fence, what is the area of the largest lot you could build?

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Answer 1 · 2015-11-04T12:21:24

#28 1/8 m^2#

Let the area be #a#
Let the length of the back of the plot be #b#
Let the length of the side of the plot be #c#

Then #2c+b=15# " so " #c=(15 -b)/2# .....(1)
#a=bc#............................................................(2)

Substitute (1) into (2) giving:

#a = (b(15-b))/2 = 15b/2 - b^2/2#

#(da)/(db) = 15/2 - b =0# at maximum area

so #color(blue)(b= 7 1/2 " metres")#

so #color(blue)(c= (15-(7 1/2))/2 " " = 3 3/4 " metres")#

#color(green)("Thus maximum area is "3 3/4 times 7 1/2 " "= " "28 1/8 m^2)#