Bob has 20 feet of fencing to enclose a rectangular garden. If one side of the garden is x feet long, he wants the other side to be (10 – x) feet wide. What value of x will give the largest area, in square feet, for the garden?
A.

3
B.

4
C.

5
D.

6

Question

Bob has 20 feet of fencing to enclose a rectangular garden. If one side of the garden is x feet long, he wants the other side to be (10 – x) feet wide. What value of x will give the largest area, in square feet, for the garden?
A.
	
3
B.
	
4
C.
	
5
D.
	
6

phemenway0001 · Answer

let 
A(x) = x(10 - x) ← area = length × width 
       = 10x - x² 
       = -(x² - 10x) 
then put into vertex form: 
        = -(x² - 10x + (-5)²) + 25 ← completing the square 
        = -(x - 5)² + 25 
which is an open downwards parabola 
with vertex: (5, 25) 
so 
answer: C. 5 
and max area is 25 ft²