Posted by **maikaya Foster** on Wednesday, April 24, 2013 at 10:29pm.

The perimeter of a paved area being built at a playground is going to be 46 meters. If the length and width are each a whole number of meters, what should the length and width of the area be to cover the greatest possible area?

- math -
**Reiny**, Thursday, April 25, 2013 at 7:40am
let the length be x

and the width be y

2x + 2y = 46

x+y = 23

y = 23 - x

area = xy

= x(23-x) = -x^2 + 23x

vertex of this parabola :

the x of the vertex is -b/(2a) = -23/-2 = 11.5

then y = 23-11.5 = 11.5

So the paved area should be a square with sides 11.5 m each , resulting in a maximum area of 132.25 m^2

(Of course , the largest rectangle for a given perimeter is always a square)

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