Find the length of the side of a square if the area is 4 inches^2 less than the perimeter.
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Let x be one side of the square.
The area of the square is:
A = x^2
The perimeter of the square is:
P = 4x
Now, we'll write mathematically the condition given by enunciation:
x^2 = 4x - 4 (area is equal to the perimeter minus 4)
We'll subtract both sides 4x - 4:
x^2 - 4x + 4 = 0
We'll recognize the perfect square:
(x - 2)^2 = 0
(x-2)(x-2) = 0
x – 2 = 0 => x = 2
The length of the side of the square is x = 2 inches.
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