Question

The length of a swimming pool is 3 feet longer than it’s width. The swimming pool is surrounded by a deck that is 2 feet wide and has an area of 116 square feet. Find the dimensions of the pool

Answer 1

The Length of swimming pool is 8.35 feet

The width of swimming pool is 5.35 feet

Explanation:

Given as :

The length of swimming pool is 3 feet longer that its width

Let The width of swimming pool = w feet

So, The Length of swimming pool = L = (w + 3) feet

Now, The swimming pool is surrounded by deck of 2 feet wide

The width of deck = w' = w + 2 + 2 = (w + 4) feet

The area of deck = 116 feet²

The length of deck = L' = L + 2 + 2 = (L + 4) feet

So, L' = (w + 3 + 4) feet

I.e L' = (w + 7) feet

∵ The area of deck = 116 feet²

So , L' × w' = 116 feet²

(w + 7)× (w + 4) = 116

Or, w² + 4 w + 7 w + 28 = 116

Or, w² + 11 w - 88 = 0

Solving the quadratic equation as

ax² + bx + c = 0

So, w =
`\frac{-b\pm \sqrt{b^(2)-4* a* c}}{2* a}`

Or, w =
`\frac{-11\pm \sqrt{11^(2)-4* 1* (-88)}}{2* 1}`

Or, w =
`(-11\pm √(473))/(2)`

or, w =
`(-11\pm 21.7)/(2)`

or, w = 5.35 , -16.35

The width of swimming pool = w = 5.35 feet

The Length of swimming pool = L = (5.35 + 3) feet = 8.35 feet

Hence, The Length of swimming pool is 8.35 feet

And The width of swimming pool is 5.35 feet

Answer