Reggie currently has a square rug in his living room. He is moving soon and has determined that for his new living room, he will need a rug that has a width that is two feet shorter than his current rug and a length that is five feet longer than his current rug. Let x represents the side measure of Reggie's current rug, in feet. Determine the equation that represents the area, y, in square feet, of the rug needed for his new living room.

Reggie currently has a square shaped rug in his living room. The side lengths of square are all equal. The length of a side of a square is given to be x feet.

So length and width of current rug are x feet and x feet respectively.

For his new room, he needs a rug that is 2 feet shorter in width than his current rug. So the width of new rug will be (x - 2) feet. The length of his new rug will be 5 feet more than the length of his current rug. So the length of new rug will be (x + 5) feet.

The new rug will have unequal length and width, hence it will be rectangular in shape. The area of new rug will be:

Area = Length x Width

y = (x + 5) (x - 2) square feet

This equation represents the Area of the rug Reggie needs for his new room.