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

${(x - 1)}^{2} = 8$ $(x-1)^2 =8$

$x = 1.828$ $x = 1.828$ 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 $x$ $x$ units,

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

The area of a square is found from $side \times side$ $"side" xx" side"$

$A = s \times s = (x - 1) (x - 1)$ $A = s xx s = (x-1)(x-1)$

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

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

We can solve the equation:

${(x - 1)}^{2} = 8$ $(x-1)^2 =8$

$x - 1 = \sqrt{8} \leftarrow$ $x-1 = sqrt8" "larr$ only consider the positive root,

$x = \sqrt{8} - 1$ $x = sqrt8 -1$

$x = 1.828$ $x = 1.828$