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19 February, 18:28

A rectangular lawn is 24 feet wide by 32 feet long. a sidewalk will be built along the inside edges of all four sides. the remaining lawn will have an area of 425 square feet. how wide will the walk be

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  1. 19 February, 18:58
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    Area of the rectangular lawn = 24 x 32 = 768 ft²

    Given that the area of the remaining lawn = 425 ft²

    Area of the walkway = 768 - 425 = 323 ft²

    Let the width of the walkway be x.

    Area of walkway = 2 (32x) + 2 (24x) - 4 (x) ² = 64x + 48x - 4x² = 112x - 4x²

    112x - 4x² = 232

    4x² - 112x + 232 = 0

    (2x - 49) (2x - 7) = 0

    x = 49/2 or x = 7/2

    x = 24.5 (rejected, it cannot be bigger than the width) or x = 3.5

    Answer: The width of the walkway is 3.5 feet.
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