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30 October, 08:56

A rectangular porch has a width that is 7 feet less than the length. If the area of the porch floor is 120 square feet, what is the length of the width of the porch?

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  1. 30 October, 09:06
    0
    The answer to your question is width = 8 ft

    Step-by-step explanation:

    Data

    width = x - 7

    length = base = x

    Area = 120 ft²

    Process

    1. - Write the formula of the area of a rectangle

    Area = base x width

    - Substitution

    120 = x (x - 7)

    2. - Solve for x

    120 = x² - 7x

    x² - 7x - 120 = 0

    - Factor the polynomial

    - Find the prime factors of 120

    120 2

    60 2

    30 2

    15 3

    5 5

    1

    - Find two numbers that added gives - 7

    These numbers are - 15 and + 8

    - Factor

    x² - 15x + 8x - 120

    x (x - 15) + 8 (x - 15)

    (x - 15) (x + 8) = 0

    x₁ = 15 x₂ = - 8

    -The length of the base is 15 because there are no negative lengths.

    3. - Conclusion

    Base = 15

    Width = 15 - 7 = 8
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