Question

. An inground rectangular pool has a concrete pathway surrounding the pool. If the pool is 16 feet by 32 feet and the entire area of the pool including the walkway is 924 ft2, find the width of the walkway.

Answer 1

The width of walkway=3.72 feet

Explanation:

We are given that a rectangular pool has a concrete pathway surrounding the pool.

Let x be the width of walkway.

Length of outer rectangle =
`32+2x`

Breadth of outer rectangle =
`16+2x`

Length of pool=32 feet

Breadth of rectangle =16 feet

Area of pool=
`32* 16`=512 square feet .

The antire area of the pool including the walkway =924 square feet

Area of entire pool including walkway=
`(32+2x)(16+2x)`

`(32+2x)(16+2x)=924`

`512+64x+32x+4x^2=924`

`4x^2+96x+512-924=0`

`4x^2+96x-412=0`

Divide the equation by 4 then we get

`x^2+24x-103=0`

Quadratic formula for quadratic equation

`ax^2+bx+c=0`

`D=b^2-4ac`

`x=(-b\pm\sqrtD)/(2a)`

We have a=1, b=24,c=-103

By using quadratic formula we solve quadratic equation

`D=(24)^2-4* 1* (-103)`

`D=576+412=988`

`x=(-24\pm √(988))/(2)`

`x=(-24\pm 31.43)/(2)`

`x=(-24+31.43)/(2)` and
`x=(-24-31.43)/(2)`

`x=(7.43)/(2)` and
`x={-55.43}{2}`

x=3.72 and x=-27.7

The value of x=-27.7 is not possible because the width is always a natural number.

Hence, the width of walkway =x=3.72 feet.

Answer 2

For this case we have that the pool area without including the walkway isA = (16) * (32) = 512ft ^ 2
Then, we have that the entire area of the pool including the walkway is
Aw = 924 ft2.
(16 + 2w) * (32 + 2w) = 924
512 + 32w + 64w + 4w ^ 2 = 924
512 + 96w + 4w ^ 2 = 924
Solving for w> 0
-412 + 96w + 4w ^ 2 = 0
w = 3.72 ft
answer
the width of the walkway is w = 3.72 ft