Question 947519
u, the uniform width around the pool
w, the width of the pool
L, length of the pool
A, the area of just the walk area of uniform width u.
-
UNKNOWN:  u
KNOWN:  w=10, L=50, A=864


Note: sometimes, variables can be assigned differently, mostly depending on the person analyzing the problem.


Draw the picture  (not shown here).


Total Area pool and walkway:  {{{(w+2u)(L+2u)}}}
Walkway Area only:  {{{(w+2u)(L+2u)-wL}}}
Walkway Area IS known:  {{{highlight_green((w+2u)(L+2u)-wL=A)}}}


The green-highlighted equation, purely in symbolic form can be simplified and is a quadratic equation in the unknown variable, u.   The rest is up to you to continue.