A farmer has 70 meters of fencing to enclose a rectangular garden that has one side of the garden against a barn.

Question

REALLY stuck on B and C (already solved a) Thank you

A farmer has 70 meters of fencing to enclose a rectangular garden that has one side of the garden against a barn.

Let  represent the length of the rectangular garden (in meters). (Notice that the 70 meters of fencing is needed for only 3 sides of the garden.)

1. 
   
2. Suppose the length of the garden is 30 meters ().
3. 
   
4. What is the width of the garden?
5. What is the area of the garden?
6. 
   
7. 
   
8. B: Write an expression in terms of  that represents the width of the garden (in meters).
9. 
   
10. 
    
11. C: Write an expression in terms of  that represents the area of the garden (in meters).

Answer 1

(B) L + 2w = 70

2w = 70 - L

w = (70 - L)/2

(C) Area as a function of L:

Area = length * width

= L * (70-L)/2

As you said part A is done, when L=30, the width is (70-30)/2 = 40/2 = 20,

the area is 30*20 = 600 and the perimeter is 2*(20 + 30) = 2*50 = 100