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Find the length of the side of a square if the area is 4 inches^2 less than the perimeter.

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portoruj | Student, Grade 10 | eNoter

Posted April 17, 2011 at 11:55 PM via web

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Find the length of the side of a square if the area is 4 inches^2 less than the perimeter.

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giorgiana1976 | College Teacher | Valedictorian

Posted April 18, 2011 at 12:01 AM (Answer #1)

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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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