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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