Rectangular pool

Question

Rectangular pool that measure 18 feet by 9 feet Deck around pool: how wide should the deck be? Total area of pool and deck is 400 square feet What is the width of the deck?

Answer 1

Let.....

x=width of deck around pool

 

Then the length and width of pool plus deck is...

L=2x+18......with width of deck "x" added to either side L

W=2x+9.......with width of deck "x" added to either side W

A=400ft².......total area of pool plus deck, prob statement, given

 

A=L(W)

400=(2x+18)(2x+9)...substitute for "L" and "W"

400=4x²+54x+162.....expand using FOIL

    0=2x²+27x-119......subtract 400 each side, divide both sides by 2

 

Now use the quadratic formula to solve for "x"......

      -b±√(b²-4ac)
r= -----------------    where........
             2a

 

a=2, b=27, c=-119

 

I will leave the substitution and simplification of the quadratic

equation to you. You should arrive at two values for "x"....

x=3.5

x=-17.....disregard this value as we are solving for distance and 

              distance cannot be negative.

 

So x=3.5ft is our solution.  Lets check our answer by subsitiuting

our value into the dimension expressions and area equation....

L=2(3.5)+18=7+18=25ft
W=2(3.5)+9=7+9=16ft

    A=LxW

400=25(16)

400=400.......√check, our solution "X=3.5ft" is correct.

 

Always check your work!