orumsCalendar Gradebook sment ons of Quadratic Equations A farmer needs to enclo

Question

orumsCalendar Gradebook sment ons of Quadratic Equations A farmer needs to enclose three sides of a pasture with a fence (the fourth side is a cliff wall). The farmer has 28 yards of fence and wants the pasture to have an area of 96 sq-yards. What should the dimensions of the pasture be? (For the purpose of this problem, the width will be the smaller dimension (needing two sides; the length with be the longer dimension (needing one side). Additionally, the length should be as long as possible.) lengthyards widthyards Enter your answers as numbers. If necessary, round to the nearest hundredths Get help, worked Example 1 Points possible: 1 Unlimited attempts Submit

Explanation / Answer

let length = l and width = w

there is fencing on 2 widths and 1 length

so setting up the equation

2w + l = 760

l = 760 - 2w

area = length * width

= ( 760 - 2w ) w

= 760 w - 2w^2

maximum area occurs at

w = - 760 / -2(2)

w = 190

l = 380

shorter side = 190 ft

longer side = 380 ft

greatest area = 72200 ft^2

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