Question 1006038
Let {{{ A }}} = area of original rectangle
The formula for perimeter is:
{{{ P = 2L + 2W }}}
{{{ 36 = 2L + 2W }}}
{{{ L + W = 18 }}}
{{{ L = 18 - W }}}
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Let {{{ A }}} = area
{{{ A = L*W }}}
{{{ A = ( 18 - W )*W }}}
{{{ A = 18W - W^2 }}}
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You are given that:
{{{ A + 30 = ( L + 1 )*( W + 2 ) }}}
{{{ A + 30 = ( 18 - W + 1 )*( W + 2 ) }}}
{{{ A + 30 = ( -W + 19 )*( W + 2 ) }}}
{{{ A = -W^2 + 19W - 2W + 38 - 30 }}}
{{{ A = -W^2 + 17W + 8 }}}
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By substitution:
{{{ 18W - W^2 = -W^2 + 17W + 8 }}}
{{{ 18W = 17W + 8 }}}
{{{ W = 8 }}}
and
{{{ L = 18 - W }}}
{{{ L = 18 - 8 }}}
{{{ L = 10 }}}
and
{{{ A = L*W }}}
{{{ A = 10*8 }}}
{{{ A = 80 }}}
The original area was 80 m2
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check:
{{{ A + 30 = ( L + 1 )*( W + 2 ) }}}
{{{ A + 30 = (10 + 1 )*( 8 + 2 ) }}}
{{{ A = 11*10 - 30 }}}
{{{ A = 110 - 30 }}}
{{{ A = 80 }}}
OK