SOLUTION: A rectangular pool measures 10m by 5m. A deck, of uniform width, is to be built all the way around the pool such that the total area of the pool and deck will be 126m^2. Set up and

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A rectangular pool measures 10m by 5m. A deck, of uniform width, is to be built all the way around the pool such that the total area of the pool and deck will be 126m^2. Set up and      Log On


   

Question 171384: A rectangular pool measures 10m by 5m. A deck, of uniform width, is to be built all the way around the pool such that the total area of the pool and deck will be 126m^2. Set up and solve a quadratic equation to determine the width of the deck.
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let w=width of the deck
Area of the pool and deck is:
(10+2w)(5+2w)=50+30w+4w^2 and we are told that this equals 126m^2, so:
4w^2+30w+50=126 subtract 126 from each side
4w^2+30w-76=0 divide each term by 2
2w^2+15w-38=0---------------quadratic in standard form; solve using quadratic formula:
w+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
w+=+%28-15+%2B-+sqrt%28+225%2B304%29%29%2F%284%29+
w+=+%28-15+%2B-+%2823%29%29%2F%284%29+
Neglect negative value for w; widths in this case are positive, so:
w=8%2F4=2+m-------------------width of deck
CK
(10+4)(5+4)=126
14*9=126
126=126
Hope this helps---ptaylor