what is the width of the patio?

Question

Caroline has a patio of uniform width around the perimeter of her rectangular pool. The pool measures
22 ft by 12 ft. If the area of the pool and the patio is 504 ft , what is the width of the patio?

Answer 1

Let x = width of the patio, therefore the length and width of the patio/pool is 22+2x and 12+2x.  Set up the area equation:

 

(22+2x)(12+2x)=504  Divide everything by 2

 

(11+x)(6+x) = 252  Multiply out and combine like terms

 

x² + 17x - 186 = 0 Solve witht he quadratic formula

 

[-17 +/- sqrt(289 - 4(1)(-186))]/2

 

[-17 +/- 32.14]/2  the negative answer will not work so the answer is 7.57