Question

I think I have the correct answers but will anyone try to solve these questions so I can see if we got the same answer.

Answer 1

Because you seem to have an understanding of the material, I will write my math, but no explanations for my work. Comment on this answer for an explanation, or if I did something wrong.

1. Find the length of the South side of the field.

`(5x+2)+(x^2-9)+(x^2-7x+12)\\5x+2+x^2-9+x^2-7x+12\\2x^2+5x+2-9-7x+12\\2x^2-2x+2-9+12\\2x^2-2x+5`

2.Find the perimeter of the pumpkin field.

`2(5x+2)+2(5x-2)\\(5x+2)+(5x+2)+(5x-2)+(5x-2)\\20x+4-4\\20x`

3. Find the perimeter of the whole field.

`2(4x+5x-2)+2(5x+2+x^2-9+x^2-7x+12)\\2(9x-2)+2(2x^2-2x-5)\\18x-4+4x^2-4x+10\\4x^2+14x+6`

4. If
`x=30ft`, what is the total perimeter?

`P=4x^2+14x+6\\P=4(30)^2+14(30)+6\\P=4(900)+420+6\\P=1026ft`

Random Tangent:

If you want to involve
`y` in finding these answers for whatever reason, your math is going to get messy. Here's what I tried before I realized you could multiply each side by
`2` to get the total perimeter:

`xy+1+x+6=4x+5x-2\\xy-8x=-9\\x(y-8)=-9\\y-8=-(9)/(x)\\y=-(9)/(x)+8`

Now the other side. This one's even worse.

`xy-1+6x+x=5x+2+x^2-9+x^2-7x+12\\xy+9x-2x^2=5\\x(y+9+2x)=5\\2x+9+y=(5)/(x)\\y=(5)/(x)-2x-9`

At this point, was realizing I wasn't going about the problem correctly, but did one last try by setting
`y=y`. At this point in the equation, I simply had to stop, both due to complexity and technological problems.

`(5)/(x)-2x-9=-(9)/(x)+8\\(14)/(x)=2x+17\\ 14=2x^2+17x\\0=2x^2+17x-13\\`

I could possibly continue to solve, but I don't see a point. It was clear that this was NOT the right path to take finding the perimeter. It was here I realized that I could just multiply the two sides without
`y` in them by
`2` and--without as much difficulty--reach the correct answer.