The width and the length of a rectangle are consecutive even integers. If the width is decreased by 3 inches, then the area of the resulting rectangle is 24 square inches. What is the area of the original rectangle

  48 square units

Step-by-step explanation:

Let L and W represent the length and width of the rectangle.

  L = W +2 . . . . . . assuming the length is more than the width

  L(W -3) = 24 . . . . the area after the reduction in width

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  (W +2)(W -3) = 24

So, we're looking for factors of 24 that differ by 5. We know that 24=8·3, so we have ...

  W+2 = 8

  W = 6 . . . . . . . matches W-3=3, also

Then the length is ...

  L = W+2 = 8

and the area of the original rectangle is ...

  A = LW = (8 inches)(6 inches) = 48 square inches

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