need answer for this question asap

Question

A gardener has 520 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river and so it does not need any fencing.

  

What dimensions would guarantee that the garden has the greatest possible area? 

shorter side:    _____ft (feet)

longer side: ____ft (feet)

greatest possible area: ___ft²  (square-feet)

Answer 1

The constraint on the length (along river) and width is the length of fencing, F: 2W + L = F

The area that you want to maximize is LW = A

Solving for L in the constraint, and substituting into the Area equation, one obtains:

(F-2W)(W) = A or -2W²+FW-A=0 or W²-(F/2)W+A/2 = 0

You can set the derivativeof A(W) to zero and find the W for maximum A or you can just find the vertex of the parabola written above (which is at W = F/4) (This is general for this situation of a rectangular fence with one side provided by a wall or river (W=F/4 and L=F/2 - In the case of a rectangle with only the fence providing the barrier, the answer is a square with side = F/4)

Answer 2

w represents the width of the garden

520 - 2w represents the length of the garden

w(520 - 2w) represents the area of the garden

A = w(520 - 2w)

Can you convert to vertex form (from Algebra 1) and answer?