Question

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?

Answer 1

Answer:

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