Question

A square pool has a side length of x feet.A uniform border around pool is 1 footwide.The total area of the pool and the border os 361 square feet.What is the area of the pool

Answer 1

The total area of pool and border = 361  square feet.

Length of square pool = x

Length of square pool plus border =  (x + 1 +1 ) = x + 2

There is 1 foot length on each side on the x  length.

The other length of the square pool and border =  (x + 2)

Area = (x+2)(x+2)

     (x + 2)(x +2) =  361.            Let A = x +2

        A*A = 361
            A²  = 361    Take square root of both sides
             A  = √361
               A = 19

A = x + 2 = 19
       x = 19 - 2
       x = 17

Area of square pool = x*x = 17*17 = 289

Area of the pool = 289 square feet.

Answer 2

The area of the pool is required.

The area of the pool is $289\ \text{feet}^2$

Let the side of the pool be $x$

When a uniform 1 feet wide border is present surrounding the pool the area would be

$(x+1+1)^2=(x+2)^2$

Now area of pool with boundary is 361 square feet

$(x+2)^2=361\\\Rightarrow x+2=\pm 19\\\Rightarrow x=19-2,-19-2\\\Rightarrow x=17$

The length of the side of the pool is 17 feet

Area of the pool is

$17\times 17=289\ \text{feet}^2$

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