A rectangular pool measures 5 yd by 6 yd. A concrete deck of uniform width is constructed around the pool. The deck and pool together cover an area of 72 yds². How wide is the deck?

Common sense would say that if you add 3 yds onto the pool dimensions, that would create a width of 8 and length of 9, which would make the area 72 yds². Here is the algebraic proof:

(x + 5)(x + 6) = 72 {multiplied width x length and set equal to area of 72}

x² + 11x + 30 = 72 {used foil method / distributive property}

x² + 11x - 42 = 0 {subtracted 72 from each side}

(x + 14)(x - 3) = 0 {factored into two binomials}

x + 14 = 0 or x - 3 = 0 {set each factor equal to zero}

x = -14 or x = 3 {solved each equation for x}

**width of pool = 5 yds**

length of pool = 6 ydslength of pool = 6 yds

**x = width of deck****x + 5 = width of pool + width of deck**

x + 6 = length of pool + width of deckx + 6 = length of pool + width of deck

(x + 5)(x + 6) = 72 {multiplied width x length and set equal to area of 72}

x² + 11x + 30 = 72 {used foil method / distributive property}

x² + 11x - 42 = 0 {subtracted 72 from each side}

(x + 14)(x - 3) = 0 {factored into two binomials}

x + 14 = 0 or x - 3 = 0 {set each factor equal to zero}

x = -14 or x = 3 {solved each equation for x}

*width of deck cannot be -14***width of deck = 3 yds**

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