Question

Fred and Sue want to fence in a rectangular area in their yard for a vegetable garden. Suppose that they have 30 feet of fencing. Sue tells Fred that she wants to put up the fence in such a way as to obtain a rectangular garden with the largest possible perimeter. Fred replies that the perimeter will be the same for any rectangular garden that they construct as long as they use all of the fencing. Is Fred correct? Explain.

Answer 1

Answer:

Yes, Fed is correct

Explanation:

We only get 30 feet of fencing, it is already the largest possible perimeter that we can do if we use all of the fencing.

Answer 2

Answer:

a=35x−x^2

Step-by-step explanation:

Having  

70 ft of fencing with a  

width of x

feet and knowing the perimeter of a rectangle is  

p=2w+2l

we can state the length of the garden as:

70=2x+2l

and solving for  l

we know the length with be:

2l=70−2x or l=35−x  

And then knowing the formula for the area of a rectangle is  

a=w⋅l

we can write the equation as:

a=x⋅(35−x)a=35x−x^2