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11 October, 06:19

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?

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  1. 11 October, 08:47
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    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

    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

    therfor width of walkway=3ft
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