Bob has 40 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 (20 - x) feet wide. What value of x will give the largest area, in square feet, for the garden? A. 8 B. 9 C. 10 D. 11

One way to do this is to try the different option to replace x. Let's start with 8. Two sides of the rectangle would be 8.

8*2=16

Now you have to take 16 from 40 to see what's left.

40-16=24

2 (20-8) = 2 (12) = 24

That means 8 is an option to use, but you still need to see if any of the other options work to find the greatest area.

9*2=18 ... 40-18=22 ... 2 (20-9) = 2 (11) = 22

9 would also work.

10*2=20 ... 40-20=20 ... 2 (20-10) = 2 (10) = 20

10 would work

11*2=22 ... 40-22=18 ... 2 (20-11) = 2 (9) = 18

So all of them would work. Now you just need to find the largest area, which is length x width.

x (20-x)

8 (20-8) = 8 (12) = 96

9 (20-9) = 9 (11) = 99

10 (20-10) = 10 (10) = 100

11 (20-11) = 11 (9) = 99

So if x is 10, It would make the largest area.

(Sorry for all the extra work. I never trust that all the answers would work for the perimeter)