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?

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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