How to find an equation for the area of a square?

Question

If the length of a square is decreased by 1 unit, the area is now 8 square units. What's the equation for the area of this square.

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Answer 1 · 2018-06-06T19:11:09

#(x-1)^2 =8#

#x = 1.828# units was the original length of the square.

First choose a variable to use in writing an equation,

Let the original length of the square be #x# units,

If it has been decreased by #1# units, the new length is #x-1# units.

The area of a square is found from #"side" xx" side"#

#A = s xx s = (x-1)(x-1)#

The new area is # 8# square units, Write the equation:

#A= (x-1)(x-1) =8#

We can solve the equation:

#(x-1)^2 =8#

#x-1 = sqrt8" "larr# only consider the positive root,

#x = sqrt8 -1#

#x = 1.828#