Answer:
width of the sidewalk = 1 feet
Step-by-step explanation:
Area of the pool = length × width
Length = 10 feet
Width = 6 feet
Area of the pool = length × width
= 10 feet × 6 feet
= 60 feet²
Area of the pool = 60 feet²
Total area = Area of the pool + Area of sidewalk
96 feet² = 60 feet ² + Area of sidewalk
Area of sidewalk = 96 feet² - 60 feet ²
Area of sidewalk = 36 feet²
Length of pool + sidewalk = 10 + 2x
width of pool + sidewalk = 6 + 2x
( 10 + 2 x ) ( 6 + 2 x ) -60 = 36
60 + 20x + 12x + 4x² - 60 = 36
4x² + 32x - 36 = 0
4x² + 36x - 4x - 36 = 0
4x (x + 9) -4(x + 9) = 0
(4x - 4) (x + 9) = 0
4(x - 1) (x + 9) = 0
(x - 1) = 0 (x + 9) = 0
x = 1 or x = -9
The width of the side walk can't be a negative value
Therefore, width of the sidewalk = 1 feet
A rectangular pool has a sidewalk around it. Width of the sidewalk is 1 feet.
Given
A rectangular pool has a sidewalk around it. The pool measures 6 feet by 10 feet and the total area of the pool and sidewalk is 96 square feet.
Let 'w' be the width of sidewalk
The pool measures 6 feet by 10 feet . The width of the rectangular pool with side walk is 6+x+x=6+2x
The length of the rectangular pool with side walk is 10+2x
The total area of the pool and side walk is length times width
Total area= [tex](6+2x)(10+2x)\\[/tex]
[tex]96=(6+2x)(10+2x)\\96=60+32x+4x^2\\60+32x+4x^2-96=96-96\\4x^2+32x-36=0[/tex]
apply quadratic formula to solve for x
[tex]x=\frac{-32\pm \sqrt{32^2-4\cdot \:4\left(-36\right)}}{2\cdot \:4}\\x=\frac{-32\pm \:40}{2\cdot \:4}\\x= \frac{-32+40}{2\cdot \:4}=1\\x=\frac{-32-40}{2\cdot \:4}=-9[/tex]
Width of the sidewalk cannot be negative
so the width of the sidewalk is 1 feet
Learn more : brainly.com/question/21860114
