SOLUTION: A square playing field is to be changed to a rectangular shape by adding 2 m to the length and subtracting 2 m from the width. Determine which playing field has the larger area: t

Question 1022701: A square playing field is to be changed to a rectangular shape by adding 2 m to the length and subtracting 2 m from the width. Determine which playing field has the larger area: the original square field or the new rectangular field. What is the difference in area?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let the side of the square playing field be called x.

the area of the square playing field is equal to side * side which is equal to side squared which is equal to x^2.

since it is square, the length and the width are both equal to x.

add 2 meters to the length and you get a length of x + 2.

subtract 2 meters from the width to get a width of x - 2.

the area of the rectangular playing field is equal to length * width which is equal to (x + 2) * (x-2) which is equal to x^2 - 4.

the area of the square playing field is greater than the area of the rectangular playing field by 4 meters.

x^2 minus (x^2 - 4) = x^2 - x^2 + 4 = 4.

the difference in the area will always be 4 meters, regardless of the value of x.

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