ap calc

posted by .

A pool, that is 12 feet wide and 18 feet long, is to have a sidewalk of uniform length constructed around its perimeter.

a. write the equation for the area A, of the pool with the sidewalk

b. determine the domain of the area of the pool with the sidewalk

c. what would the width of the sidewalk need to be in order for the area to be 364 sq. ft.

I am confused about what they want and not sure how to begin. If you could guide me, I would appreciate it.

  • ap calc -

    OOPS, I meant Pre-Calc not ap Calc sorry

  • ap calc -

    Draw the pool as a rectangle.

    Now draw a rectangle around that, such that each side is equally distant from the sides of the pool. This represents the sidewalk around the pool.

    The area of the pool is 12 * 18 = 216 sq.ft.

    If the sidewalk were 3 feet wide everywhere, the width of the whole area would be (12 + 3 + 3) and the length (18 + 2 + 3). But we don't know the width, so call it x.

    Now the width is:
    12 + x + x = 12 + 2x

    Fill in the length yourself similarly.

    Now, the equation for the area of the whole thing is:

    A = (2x + 12)(length you worked out)

    Multiply that out, and you'll get a quadratic equation.

    I'm a little unsure about what the question means by b. myself. I'd be inclined to say R+, but maybe I'm missing the point.

    Given the formula you worked out in a., just set 364 = the quadratic equation, and solve for x.

    I hope this gives you enough to go on.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Physics

    A sidewalk is to be constructed around a swimming pool that measures (11.00+/-0.12) m by (17.40+/-0.12) m. If the sidewalk is to measure (1.22+/-0.02) m wide by (9.60+/-0.15) cm thick, what volume of concrete is needed?
  2. Math

    Cody has a circular fish pond with a diameter of 6.4 feet around which he wants to put a sidewalk. He has enough concrete left over to cover an area of 65 square feet. Assuming the sidewalk is of uniform width, how wide can the sidewalk …
  3. Math

    Need help on the question below. A pool has a diameter of 12 ft. There is a sidewalk that extends 3 ft out from the side of the pool. How many feet of fencing will be needed to go around the sidewalk?
  4. Algebra

    The Roice family have a rectangular swimming pool. It measures 16' x 32'. This summer they are installing a sidewalk around the pool. The width of the sidewalk is yet to be determined, 1) Using the x as the width of the sidewalk, write …
  5. Math

    The length of a rectangular pool is to be four times its width, and a sidewalk 6 feet wide will surround the pool. If a total area of 1440 𝑓𝑡 2 has been set aside for construction, what are the dimensions of the pool?
  6. Geometry

    mr james has a swimming pool in his backyard that is 10 ft by 15 ft he wants to put a concrete sidewalk with uniform width around his pool so that the pool and sidewalk cover a combined area in his backyard of 336 ft ^2. What is the …
  7. Math

    Sally wants to build a fence around her pool. The pool is 26 feet long by 21 feet wide. The fence is to be 15 feet from the edge of the pool. What are the outside dimensions of the area surrounding the pool?
  8. Math

    Sally wants to build a fence around her pool. The pool is 26 feet long by 21 feet wide.The fence is to be 15 feet from the edge of the pool. a.What are the outside dimensions of the area surrounding the pool?
  9. Math

    Sally wants to build a fence around her pool. The pool is 26 feet long by 21 feet wide.The fence is to be 15 feet from the edge of the pool. a.What are the outside dimensions of the area surrounding the pool?
  10. Math

    A rectangular swimming pool is 6 meters longer than the width of the pool. A pool deck (sidewalk) that surrounds the pool is 4 meters wide (all the way around the pool). The combined area of the pool deck and pool together (outer rectangle) …

More Similar Questions