Arectangle is drawn so that the width is 4 feet shorter than the length. the area of the rectangle is 45 square feet. find the length of the rectangle.

  9 ft

Step-by-step explanation:

Since you're familiar with your multiplication tables, you know that ...

 45 = 5×9

These factors differ by 4, so correspond to the width and length of the rectangle.

The length of the rectangle is 9 feet.

Seeing this solution, you might wonder, "how do I do this in the case where I don't know the factors of the number?" If the problem has an integer solution, that solution will be a factor of the number, so going to the trouble to determine the number's factors is part of the solution process.

If the solution is not an integer, then you will need to write and solve the appropriate quadratic equation. Here the problem asks for length. We can make that x, so the width is (x-4) and the area is ...

  x(x -4) = 45

Expanding this and completing the square (one of several methods of solving quadratic equations), you get ...

  x² -4x = 45

  x² -4x +4 = 49 . . . . . . add the square of half the x-coefficient

  (x -2)² = 49 . . . . . . . . . show as a square

  x -2 = ±7 . . . . . . . . . . . take the square root

  x = 2±7 . . . . . only x=9 is useful in this problem

The length of the rectangle is 9 feet.

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