A rectangular pool is 30 feet wide and 40 feet long. It is surrounded on all four sides by a wooden deck that is x feet wide. The total area

Question

A rectangular pool is 30 feet wide and 40 feet long. It is surrounded on all four sides by a wooden deck that is x feet wide. The total area enclosed within the perimeter of the deck is 2000 square feet. What is the width of the deck?

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Mia 3 weeks 2021-12-31T01:53:51+00:00 1 Answer 0 views 0

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    2021-12-31T01:55:40+00:00

    Answer:

    5 feet

    Step-by-step explanation:

    We are given that

    Width of rectangular pool=b=30 feet

    Length of rectangular pool=l=40 feet

    Area of rectangle=l\times b

    Using the formula

    Area of rectangular pool=30\times 40=1200ft^2

    Total area enclosed within the perimeter of  the deck=2000ft^2

    Width of deck=x ft

    Length of rectangular pool including wooden deck=40+2x ft

    Width of  rectangular pool including wooden deck=30+2x ft

    Area of rectangular pool including wooden deck=(40+2x)(30+2x)

    According to question

    (40+2x)(30+2x)=2000

    40(30)+2x(30)+40(2x)+2x(2x)=2000

    1200+60x+80x+4x^2=2000

    140x+4x^2=2000-1200=800

    4x^2+140x-800=0

    x^2+35x-200=0 (Dividing by 4 on both sides)

    x^2+40x-5x-200=0

    x(x+40)-5(x+40)=0

    (x+40)(x-5)=0

    x+40=0

    x=-40

    It is not possible because width cannot be negative it is always natural number.

    x-5=0\implies x=5

    Hence, the width of the deck=5 ft

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