.Bob wants toants to use it all. If the garden is to be x feet wide, express the area of the garden as a function of x.

Question

Bob wants to fence in a rectangular garden in his yard. He has 70 ft of fencing to work with and wants to use it all. If the garden is to be x feet wide, express the area of the garden as a function of x.

Answer 1

Hello, Christen

 

Let x be the width of the garden

Let l be the length of the garden. 

l= 35-x

 

area= l*w

area= (35-x) x

area = 35x-x^2

 

Why???  The formula for the perimeter of a rectangle is

p= 2w+2l            Solving for l

-2w   -2w            Subtracting 2w from both sides.  We are trying to isolate the variable l.

(p-2w)=2l           dividing both sides by 2, since we are interested in l not 2l.

(p-2w)/2=(2l)/2

(p-2w)/2=l         Substituting 70 for p, which is the perimeter

(70-2w)/2=l       Dividing the left side by 2

35-w= l              Substituting x for w

35-x=l

 

So, there you have it.  I hope this helps out. Don't forget to rate my answer. :)

 

D. Y. Taylor