Answer:
[tex]8\text{ feet}[/tex]
Step-by-step explanation:
GIVEN: A pool measuring [tex]12[/tex] meters by [tex]30[/tex] meters is surrounded by a path of uniform width. If the area of the pool and path combined is [tex]1288[/tex] square meters.
TO FIND: Width of the path.
SOLUTION:
Consider the figure attached.
let the width of the path be [tex]=x[/tex]
Total width of pool including pool [tex]=12+2x[/tex]
Total length of pool including pool [tex]=30+2x[/tex]
Now,
Area of pool and path combined [tex]=1288\text{ sq m}[/tex]
area of pool and path combined [tex]=(\text{length})\times\text{width}[/tex]
[tex]=(30+2x)\times(12+2x)[/tex]
[tex](30+2x)\times(12+2x)=1288[/tex]
[tex]{x}^2+21x-232=0[/tex]
solving equation we get [tex]x=8\text{ feet}[/tex]
Hence the width of the path is [tex]8\text{ feet}[/tex]
