Question

The length of a swimming pool is 3 feet longer than it's width. The swimming pool is surrounded by a deck that is 2 feet wide and has an area of 116 square feet. Find the dimensions of the pool

Answer 1

Answer:

The Dimension of the pool is approximately 5.37 feet and 8.37 feet.

Step-by-step explanation:

Given:

Area of Swimming Pool = 116 sq. ft

The length of a swimming pool is 3 feet longer than it's width.

Let the width of swimming pool be 'x' feet.

∴Length  = $3+x$ feet

Also given :

The swimming pool is surrounded by a deck that is 2 feet wide.

Hence we can say the deck is surrounded 2 feet on all 4 sides.

hence;

Length of swimming pool  will become = $3+x+4 = 7+x$

Width of swimming pool will become = $x+4$

Since Swimming pool is in rectangular shape.

Now we know that area of Swimming pool is equal to length multiplied by width.

Framing in equation form we get;

$\textrm{Area of Swimming Pool}= length \times width$

Substituting the given values we get;

$(x+7)(x+4)=116$

Solving the equation we get;

$x^2+4x+7x+28=116\\\\x^2+11x+28-116=0\\\\x^2+11x- 88 = 0$

Now solving this equation by using quadratic formula we get;

According to the Quadratic Formula,  x  , the solution for  $ax^2+bx+c  = 0$  , where  a, b  and c are numbers, often called coefficients, is given by :

$x = \frac{-b\±\sqrt{b^2-4ac}}{2a}$

in our case a = 1 , b = 11 and c = -88

$b^2-4ac = 11^2-4\times 1\times -88 = 121+352 = 473$

$x= \frac{-11\±\sqrt{473}} {2\times1}$

$\sqrt{473}$, rounded to 4 decimal digits, is  21.7486.

$x=\frac{-11\±21.7486}{2}$

Two real solutions:

$x=\frac{-11+21.7486}{2} = 5.374\ ft$

OR

$x=\frac{-11-21.7486}{2} = -16.374\ ft$

Since width of the swimming pool cannot be negative value

hence we will consider $x=5.374$

Rounding to nearest hundred we get;

Width of Swimming pool = 5.37 feet

Length of Swimming pool = 3+5.37 =8.37 feet

Hence The Dimension of the pool is approximately 5.37 feet and 8.37 feet.