Question 1104022
Let {{{ w }}} = the width of the painting
{{{ w + 10 }}} = the length of the painting
{{{ w*( w + 10 ) }}} = the area of the painting
{{{ ( w + 6 )*( w + 10 + 6 ) }}} = the area of painting plus frame
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{{{ ( w + 6 )*( w + 16 ) - w*( w + 10 ) = 402 }}}
{{{ w^2 + 6w + 16w + 96 - w^2 - 10w = 402 }}}
{{{ 12w = 402 - 96 }}}
{{{ 12w = 306 }}}
{{{ w = 25.5 }}}
and
{{{ w + 10 = 35.5 }}} = length of the painting
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The dimensions are 25.5 x 35.5
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check:
{{{ ( w + 6 )*( w + 16 ) - w*( w + 10 ) = 402 }}}
{{{ 25.5 + 6 )*( 25.5 + 16 ) - 25.5*35.5 = 402 }}}
{{{ 31.5*41.5 - 905.25 - 402 }}}
{{{ 1307.25 - 905.25 = 402 }}}
{{{ 402 = 402 }}}
OK