Question 1137206
Let {{{P }}} = perimeter
Let {{{ A }}} = area
Let {{{ a }}} = length
Let {{{ b }}} = width
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{{{ P = 2a + 2b }}} m
{{{ 2a + 2b = 44 }}}
(1) {{{ a + b = 22 }}}
and
{{{ A = a*b }}} m2
(2) {{{ a*b = 105 }}}
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(1) {{{ b = 22 - a }}}
(2) {{{ a*( 22 - a ) = 105 }}}
(2) {{{ a^2 - 22a = -105 }}}
(2) {{{ a^2 - 22a + (22/2)^2 = -105 + (22/2)^2 }}}
(2) {{{ a^2 - 22a + 121 = -105 + 121 }}}
(2) {{{ ( a - 11 )^2 = 16 }}}
(2) {{{ a - 11 = -4 }}} ( +square root of 16 gives the wrong answer )
(2) {{{ a = 7 }}}
and
(1) {{{ b = 22 - 7 }}}
(1) {{{ b = 15 }}}
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The dimensions are 7m by 15m
check:
{{{ 105 = a*b }}}
{{{ 105 = 7*15 }}}
{{{ 105 = 105 }}}
OK