The length of each side of a square is increased by 6 inches, so the perimeter is now 36 inches. What is the original length of each side of the square?

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Answer 1 · 2017-08-17T21:03:58

See a solution process below:

First, let's call the original length of each side of the square: #x#

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The perimeter of a square can be calculated as:

#p = 4x#

We know each side of the square was increased by 6 inches, so the new length of a side is:

#x + 6#

and we know the new perimeter is now 36 inches.

We can substitute this into the formula and solve for #x# as follows:

#36 = 4(x + 6)#

#36 = (4 xx x) + (4 xx 6)#

#36 = 4x + 24#

#36 - color(red)(24) = 4x + 24 - color(red)(24)#

#12 = 4x + 0#

#12 = 4x#

#12/color(red)(4) = (4x)/color(red)(4)#

#3 = (color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4))#

#3 = x#

#x = 3#

The original length of each side of the square was 3 inches.