Question 761792
The square with side = {{{ x }}} cm
has area {{{ A[1] = x^2 }}} cm2
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The square with side = {{{ x + 4 }}} cm
has area {{{ A[2] = ( x+4 )^2 }}} cm2
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given:
{{{ A[1] + A[2] = x^2 + ( x + 4 )^2 }}}
Let {{{ A = A[1] + A[2] }}}
{{{ A = x^2 + ( x + 4 )^2 }}}
{{{ A = x^2 + x^2 + 8x + 16 }}}
{{{ A = 2x^2 + 8x + 16 }}}
{{{ A = 656 }}} cm2
{{{ 2x^2 + 8x + 16 = 656 }}}
{{{ 2x^2 + 8x = 640 }}}
{{{ x^2 + 4x = 320 }}} ( This is the equation )
I can complete the square
{{{ x^2 + 4x + ( 4/2 )^2 = 320 + ( 4/2 )^2 }}}
{{{ x^2 + 4x + 4 = 324 }}}
{{{ ( x + 2 )^2 = 18^2 }}}
{{{ x + 2 = 18 }}}
{{{ x = 16 }}}
( There is also a solution {{{ x+2 = -18 }}}, but ignore it )
{{{ x + 4 = 20 }}}
The sides are 16 cm and 20 cm
check:
{{{ A[1] + A[2] = x^2 + ( x + 4 )^2 }}}
{{{ A[1] + A[2] = 16^2 + 20^2 }}} 
{{{ A[1] + A[2] = 256 + 400 }}}
{{{ A[1] + A[2] = 656 }}}
OK