Math help! This is urgent?

1.

a)

If you are given 39 m of fencing, what are the dimensions of a rectangular fence with the largest possible area?



b) If the fence is against a wall so that fencing is only needed on 3 sides, what are the dimensions of the rectangular fence with the largest possible area?



2.

a) A rectangular garden has an area of 48m squared. What are the dimensions of a rectangular garden that will used the least amount of fencing?



b) If the garden is built beside a shed so you only need fencing on three sides, what are the dimensions of the rectangular garden that will use the least amount of fencing.







PLEASE SHOW YOUR WORK AND EXPLAIN

Math help! This is urgent?
1a) The largest area is a square of side 39/4 m.



b)

Area = A*B

Perimeter = 2*A + B = 39



or



B=39-2A



Area = A*(39-2A) = -2A^2 +39A



This is a parabola, open down, with a maximum where

-4A + 39 = 0



or

A=39/4



then

B=39-2*A = 39/2



The two opposite sides have length 39/4 and the side in between is of length 39/2.



2. These questions are equivalent to #1: finding the maximum area for a given perimeter and the minimum perimeter for a given are are equivalent problems.



However, where is the square? Is it (48m)^2 or 48m^2?



Assuming the latter....



a) The garden is square sqrt(48) m by sqrt(48) m.



b) Area = (Perim/2)*(Perim/4) = Perim^2/8 = 48



implies that Perim = sqrt(8*48) = 8sqrt(6)



and the dimensions are



2sqrt(6)m by 4sqrt(6)m by 2sqrt(6)m

mask work