Question 1155671
The area of picture and frame is:
{{{ 40*60 = 2400 }}} cm2
Let {{{ A }}} = the area of the picture
{{{ 2400 - A }}} = the area of the frame
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{{{ 2400 - A = 2A }}}
{{{ 3A = 2400 }}}
{{{ A = 800 }}} cm2
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Let {{{ W }}} = the width of the frame
{{{ ( 40 - 2W )*( 60 - 2W ) = 800 }}}
{{{ 2400 - 120W - 80W + 4W^2 = 800 }}}
{{{ 4W^2 - 200W + 1600 = 0 }}}
{{{ W^2 - 50W + 400 = 0 }}}
{{{ ( W - 10 )*( W - 40 ) = 0 }}}
{{{ W }}} can't be {{{ 40 }}} since that is one of
the outside dimensions, so
{{{ W = 10 }}}
The width is 10 cm
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check:
{{{ ( 40 - 2W )*( 60 - 2W ) = 800 }}}
{{{ ( 40 - 2*10 )*( 60 - 2*10 ) = 800 }}}
{{{ ( 40 - 20 )*( 60 - 20 ) = 800 }}}
{{{ 20*40 = 800 }}}
{{{ 800 = 800 }}}
OK