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,

$x = sqrt8 -1$

$x = 1.828$