Question

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

Answer 1

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