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28 December, 23:08

Find the dimensions of the parking area if it must be 150,000 ft² where the width is 50 ft

more than a number and the length is 200 ft less than the width.

what would be the equation?

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  1. 28 December, 23:09
    0
    x² - 100x - 157500 = 0

    Step-by-step explanation:

    Let the number be x.

    Width = x + 50

    Length = x + 50 - 200 = x - 150

    Area of parking lot = 150000

    Length * Width = 150000

    (x - 150) * (x + 50) = 150000

    x * (x+50) - 150 * (x+50) = 150000

    x² + 50x - 150x - 7500 = 150000

    x² - 100x - 7500 - 150000 = 0

    x² - 100x - 157500 = 0

    (x+350) (x-450) = 0

    x - 450 = 0 {x + 350 = 0 cannot be solution as x will take a negative value}

    x = 450 ft

    Length = x - 150 = 450 - 150 = 300 ft

    Width = x + 50 = 450 + 50 = 500 ft
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