Question

A pool measuring 12 meters by 30 meters is surrounded by a path of uniform width. If the area of the pool and path combined is 1288 square meters, what is the width of the path?

Answer 1

Answer:

$8\text{ feet}$

Step-by-step explanation:

GIVEN: A pool measuring $12$ meters by $30$ meters is surrounded by a path of uniform width. If the area of the pool and path combined is $1288$ square meters.

TO FIND: Width of the path.

SOLUTION:

Consider the figure attached.

let the width of the path be $=x$

Total width of pool including pool $=12+2x$

Total length of pool including pool $=30+2x$

Now,

Area of pool and path combined $=1288\text{ sq m}$

area of pool and path combined $=(\text{length})\times\text{width}$

                                                      $=(30+2x)\times(12+2x)$

                     $(30+2x)\times(12+2x)=1288$

                     ${x}^2+21x-232=0$

                     solving equation we get $x=8\text{ feet}$

Hence the width of the path is $8\text{ feet}$