contestada

An in ground 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 walkaway is 924 ft^2, find the width of the walkway

Respuesta :

carlosego
1. Let's call:
 
 x: the width of the walkway.
 b: 2x+16 (there is a widht "x" of the walkway on each side).
 h: 2x+32  (there is a widht "x" of the walkway on each side).
 A: 924 ft^2 ( the area of the pool of including the walkway).
 
 2. The area of a rectangle is:  
 
 A=(b)(h)
 
 b: the base of the rectangle (2x+16)
 a: the height of the rectangle (2x+32)

 3. Then, we have a quadratic equation:
 
 924=(2x+16)(2x+32)
 4x^2+64x+32x+512-924=0
 4x^2+96x-412=0
 
 4. We apply the quadratic formula to find the value of "x":
 
 x=(-b±√(b^2-4ac))/2a
 
 x=3.71
 
 The answer is: The width of the walkway is 3.71 ft

The width of the walway is 3.71 ft.

Step-by-step explanation:

Given :

Area = 924 [tex]\rm ft^2[/tex]

The pool is 16 feet by 32 feet.

Solution :

let x be width of the walkway.

There is a width of the walkway on each side of the pool therefore,

base, b = 2x + 16

width, w = 2x + 32

Now, the entire area of the pool including the walkaway is,

[tex]\rm 924 = b\times w[/tex]

[tex]924 = (2x+16)\times(2x+32)[/tex]

[tex]4x^2+64x+32x+512=924[/tex]

[tex]x^2+24x-103=0[/tex]

[tex]x =\dfrac{ -24\pm\sqrt{576+412} }{2}[/tex]

[tex]x = 3.71[/tex]

The width of the walway is 3.71 ft.

For more information, refer the link given below

https://brainly.com/question/15190643?referrer=searchResults

Otras preguntas