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Richard is building a rectangular backyard from 360 feet of fencing. The fencing must cover three sides of the backyard (the fourth side is bordered by Richard's house). What is the maximum area of this backyard?

 Jul 13, 2021
 #1
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Let  two  of  the  sides    =   x    and  the  remaining side  = y

 

Perimeter   = 2x + y

360  =  2x +  y

y = 360   -2x

 

Area  =   xy

 

Area =  x  ( 360 -2x)

 

Area =    -2x^2  + 360x

 

The  area will be  maximized when   x =  -360 /  (2 * -2) =   90

 

And the  max area  =

 

xy   =

 

90  ( 360  - 2 *90)   =

 

90  ( 180)  =

 

16200  ft^2

 

 

cool cool cool

 Jul 13, 2021

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