Ahh, this question goes all the way back to my year 9 test a couple years ago; which I got wrong back then - I now know how
Firstly we find the expression for the area (using x as the walk way):
>50x * 2 (the left and right)
>20x * 2 (the top and bottom)
>4 * x^2 (the corners)
Add them all together , Area = 140x + 4x^2
Now we place the deck's area, 456 into the expression
456 = 140x + 4x^2
Solve for x
I'm a bit rusty on this i'm afraid, but I believe the only way to solve this is to factorise it
0 = 4x^2 + 140x - 456
0 = 4(x+38)(x-3) <
x must = -38 or = +3 (the numbers inside the brackets inverted)
x must = +3 as it's logical, you can't have a negative width
The walkway is 3 feet wide, we can put this into our expression to double check this,
456 = 140*(3) + 4(3)^2
456 = 420 + 4*9
456 = 420 + 36
456 = 456
Yes, 3 feet wide is correct.
*Note, I tried to keep this simple, please let me know if I didn't go into enough detail anywhere
