Ask Question
4 March, 03:21

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 2784 square feet. What is the width of the deck?

+3
Answers (1)
  1. 4 March, 04:30
    0
    Answer: the width of the deck is 18 feet

    Step-by-step explanation:

    Let x represent the width of the deck.

    If rectangular pool is 30 feet wide, it means that the total width of the pool including the wooden deck is

    (30 + x) feet

    If rectangular pool is 40 feet long, it means that the total length of the pool including the wooden deck is

    (40 + x) feet

    The total area enclosed within the perimeter of the deck is 2784 square feet. This means that

    (30 + x) (40 + x) = 2784

    1200 + 30x + 40x + x² = 2784

    x² + 70x + 1200 - 2784 = 0

    x² + 70x - 1584 = 0

    x² + 88x - 18x - 1584 = 0

    x (x + 88) - 18 (x + 88) = 0

    x - 18 = 0 or x + 88 = 0

    x = 18 or x = - 88

    since the width cannot be negative, then x = 18
Know the Answer?
Not Sure About the Answer?
Get an answer to your 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 ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers