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the length of a rectangle is 7 feet longer that the width. if the area of the rectangle is 60 square feet, find the length of the rectangle.

Sagot :

Dashataranidn

Given:

  • The length (l ) of the rectangle is 7 feet longer than the width (w ).
  • The area of the rectangle is 60 square feet.

We need to find the length of the rectangle.

Steps to find the length of the rectangle:

  1.   Express the length in terms of the width:

                           l = w + 7

  2.   Use the formula for the area of a rectangle:

                           Area = l × w

         Substitute the given area and the expression for l :

                          60 = (w + 7) × w

  3.   Form a quadratic equation:

                           60 = w² + 7w

        Rewrite in standard form:

                            w² + 7w − 60 = 0

  4.   Factorize the left side of the equation:

                           w² + 12w − 5w − 60 = 0

                           w (w + 12) −5(w + 12) = 0

                           (w + 12)(w − 5) = 0

  5.   Possible values of w :

                          w = 5

                          w = −12  (not possible because width cannot be negative)

  6.   Determine the length using the width found:

                           l = w + 7 = 5 + 7 = 12

Therefore, the length of the rectangle is:

                         [tex]\boxed{12\text{ feet}}[/tex]

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