Square perimeter.If each side of a square is increased by x units then its perimeter is increased by how many units?

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pohnpei397's profile pic

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

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If each side of a square is increased by x units, the perimeter of the square is increased by 4x units.  This is because the perimeter of a square is the sum of all four of its sides.

As an example, we have a square with sides of 1 unit each.  Its perimeter is 4 units.

Now we add 1 unit to each side.  Now each side is 2 units long.  That means the perimeter is 8.  By adding 1 unit to each side, we increased the perimeter by 4 units.  This shows that adding x units to each side results in an increase of 4x units to the perimeter.

If each side of a square is increased by x units, the perimeter of the square is increased by 4x units.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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Let's note the length of the side of the square as l.

As we know, the lengths of the sides of the square are equal.

The perimeter of the square is the sum of the lengths of the sides. Since the lengths are equal, we'll get:

P1 = 4*l

If each side is increased by x units, we'll have the new perimeter;

P2 = (l+x) + (l+x) + (l+x) + (l+x)

P2 = 4(l+x)

Now, the increasing of P2 over P1 is:

P2 - P1 = 4(l+x) - 4l

We'll remove the brackets and we'll get:

P2 - P1 = 4l + 4x - 4l

We'll eliminate like terms:

P2 - P1 = 4x

The original perimeter is 4x units smaller than the new one.

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