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.

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25-05-2018
Mathematics

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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.

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11beehshahbaz 11beehshahbaz · Answer 1 · 2018-06-03T19:22:43+02:00

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.