A rectangular pool is 20 feet wide and 50 feet long. A deck used for sunning surrounds the pool. The deck is the same width all
the way around the pool. The total area of the deck is 456 square feet. How wide is the walkway?
2 answers:
Deck=456
area of pool=legnth times width=20 times 50=1000
the area of the deck is made up of 4 rectangles and 4 squares, the rectangles' areas come in pairs
areas are
area of deck= 2(20w)+4(w^2)+2(50w)d
area of pool=legnth times width=20 times 50=1000
the area of the deck is made up of 4 rectangles and 4 squares, the rectangles' areas come in pairs
areas are
area of deck= 2(20w)+4(w^2)+2(50w)d
456=2(20w)+4(w^2)+2(50w)
distribute
456=40w+4w^2+100w
add like terms
456=4w^2+140w
divide everybody by 4
114=w^2+35w
subtract 114 from both sides
0=w^2+35w-114
find what 2 numbers multiply to get 114 and add to get 35 and factor
-3 and 38
0=(w-3)(w+38)
set each to zero
w-3=0
w=3
w+38=0
w=-38
false since measures in real life cannot be negative
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