Answer :
Dimensions should the fenced area have in order to minimize the length of fencing used is 93 feet by 62 feet.
Define area.
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.
Given,
Let x be the length
Let y be the width
Area = 5766 sq²
Area = Length ×Width
Area = x × y
5766 = x × y
y = 5766/x
Amount of fencing = x + x +y + y+ y
Amount of fencing = 2x + 3y
Amount of fencing (P ) = 2x + 3(5766/x)
Amount of fencing (P ) = 2x + 17298/x
To minimize the amount,
dP/dx = 0
2 - 17298/x² = 0
2x² = 17298
x = √8649
x = 93
Equating value of x:
y = 5766/93
y = 62
Dimensions should the fenced area have in order to minimize the length of fencing used is 93 feet by 62 feet.
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