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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

User Equi
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1 Answer

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Answer:

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

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 * 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 = (-b\±√(b^2-4ac))/(2a)

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


b^2-4ac = 11^2-4* 1* -88 = 121+352 = 473


x= \frac{-11\±√(473)} {2*1}


√(473), rounded to 4 decimal digits, is 21.7486.


x=(-11\±21.7486)/(2)

Two real solutions:


x=(-11+21.7486)/(2) = 5.374\ ft

OR


x=(-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.

User Uooo
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