What is the rule for the Area, #A m^2# of an enclosure? Full question in the description box below as an image.

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1 Answer
Sean
Jan 8, 2018

#A_(Total)=(-x^2+92x-720)# #m^2#

Explanation:

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The perimeter is:

#P=x+y+20+12+(y-20)+(x-12)=160#

#P=x+y+32+y-20+x-12=160#

#2x+2y=160#

#2(x+y)=160#

#x+y=80#

#y=80-x#

If you extend the #12#-meter side up you will divide the area into two rectangles. A larger rectangle with sides #x# and #20#, and a smaller one with sides #y-20# and #x-12#.

#A_("Large")=20x#

#A_(Small)=(y-20)(x-12)#

Since we want the area in terms of #x# we need to eliminate #y#:

#Total Area=20x+(y-20)(x-12)#

#Total Area=20x+(80-x-20)(x-12)=#

#20x+(60-x)(x-12)=20x+60x-720-x^2+12x#

#A_(Total)=(-x^2+92x-720)# #m^2#

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