SOLUTION: A swimming pool 6 meters by 10 meters long is surrounded by a walk of uniform width. The area taken up by the walk happens to equal the area of the pool. What is the width of the w

Question 826273: A swimming pool 6 meters by 10 meters long is surrounded by a walk of uniform width. The area taken up by the walk happens to equal the area of the pool. What is the width of the walk?
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
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pool dims:
x = length
y = breadth
---
outer walk dims:
u = length
v = breadth
--
walk's uniform width:
w = width
---
outer walk dims relative to pool dims:
u = (x + w) = length
v = (y + w) = breadth
---
area of pool
p = xy
---
area of walk:
w = p
w = uv - p
p = uv - p
xy = uv - xy
2xy = uv
2xy = (x + w)(y + w)
2xy = xy + wx + wy + ww
xy = wx + wy + ww
ww + (x + y)w - xy = 0
ww + (10 + 6)w - (10)(6) = 0
ww + 16w - 60 = 0
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the above quadratic equation is in standard form, with a=1, b=16, and c=-60
---
to solve the quadratic equation, by using the quadratic formula, copy and paste this:
1 16 -60
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
---
the quadratic has two real roots at:
---
w = 3.13552873
w = -19.1355287
---
negative width doesn't fit the problem statement, so use the positive root:
---
answer:
width of the walk = 3.13552873 m
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
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