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:
width of pool = 5 yds length of pool = 6 yds x = width of deck x + 5 = width of pool + width of deck x + 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 Ask the House
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