Question 388290
The diagonals of a square bisect each other at right angles. What is the length of a side of a square if the diagonals are each 12 inches long?
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Applying Pythagorean theorem:
Let x = length of one side of the square
then
{{{ x^2 + x^2 = 12^2 }}}
{{{ 2x^2 = 12^2 }}}
{{{ 2x^2 = 144 }}}
{{{ x^2 = 72 }}}
{{{ x = sqrt(72) }}}
{{{ x = sqrt(6*6*2) }}}
{{{ x = 6*sqrt(2) }}} inches
or, decimal approximation:
{{{ x = 8.49 }}} inches