Question 35738
Let x = edge of the square base.  
{{{x^2}}} = surface area of base
{{{7x}}} = surface area of each side, of which there are 4.


Total surface area = {{{x^2 + 4(7x) = 165 }}}


This is a quadratic equation, so set it equal to zero.
{{{x^2 + 28x - 165 = 0}}}


These types of problems USUALLY factor, so try to find two factors of 165 such that the difference of the numbers is 28.  Try 5 times 33!!

{{{ (x + 33)(x-5) = 0}}}

{{{x= -33}}} or {{{x = 5}}}


Reject the negative answer since a side of a box cannot be negative.  This leaves x = 5 for the side of the base.  The base is 5 cm. by 5 cm.


R^2 at SCC