Question

A rectangular pool is 20 feet wide and 50 feet long. A deck used for sunning surrounds the pool. The deck is the same width all the way around the pool. The total area of the deck is 456 square feet. How wide is the walkway?
A. 2 feet
B. 3 feet
C. 4 feet
D. 5 feet

Answer 1

The answer is b. 3 ft

Answer 2

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