Sam and Charley have a rectangular swimming pool that is 8 feet wide and 14 feet long. They are going to build a tile border around the pool

Question

Sam and Charley have a rectangular swimming pool that is 8 feet wide and 14 feet long. They are going to build a tile border around the pool of uniform width. They have 75 square feet of tile. How wide is the border?

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Julia 2 days 2021-09-09T12:48:41+00:00 1 Answer 0

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    2021-09-09T12:49:53+00:00

    Answer:

    The width of the border will be 3/2 ft or 1.5 ft

    Step-by-step explanation:

    The rectangular swimming pool is 8 ft wide and 14 ft long. A tile border is built around the pool of uniform width. The tile border is 75 ft².   The illustration below is just like a rectangle inside another rectangle.

    The tile border around the pool has a uniform width. The width was added to both end of the length and the width of the rectangular pool.

    Let

    The added width = a

    On both end the added width will be

    (8 + 2a) and (14 + 2a)

    The area of the whole rectangle formed including the border

    (8 + 2a) (14 + 2a)

    The area of the rectangular swimming pool

    8 × 14 = 112  ft²

    The area of the border(75 ft²)

    (8 + 2a) (14 + 2a)  – 112  = 75

    112 + 16a + 28a + 4a² – 112 = 75

    4a² + 44a – 75 = 0

    find the numbers you multiply to get -75 × 4 = -300 and also add to get 44. The numbers are – 6 and 50.

    4a² – 6a + 50a – 75  = 0

    2a(2a – 3) + 25(2a – 3) = 0

    (2a−3)(2a+25)

    2a – 3 = 0  or 2a + 25 = 0

    a = 3/2 or a = -25/2

    we will use a = 3/2 since it is positive.

    The width of the border will be 3/2 ft or 1.5 ft

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