Question 744333
{{{ L }}} = length in cm
{{{ W }}} = width in cm
{{{ A }}} = area in cm2
{{{ P }}} = perimeter in cm
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(1) {{{ A = L*W }}}
(2) {{{ P = 2L + 2W }}}
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given:
(1) {{{ 192 = L*W }}}
and
(2) {{{ 56 = 2L + 2W }}}
(2) {{{ L + W = 28 }}}
(2) {{{ W = 28 - L }}}
By substitution:
(1) {{{ 192 = L*( 28 - L ) }}}
(1) {{{ L^2 - 28L + 192 = 0 }}}
{{{ L = (-b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = 1 }}}
{{{ b = -28 }}}
{{{ c = 192 }}}
{{{ L = (-(-28) +- sqrt( (-28)^2 - 4*1*192 )) / (2*1) }}}
{{{ L = ( 28 +- sqrt( 784 - 768 ) ) / 2 }}}
{{{ L = ( 28 +- sqrt( 16 ) ) / 2 }}}
{{{ L = ( 28 - 4 ) / 2 }}}
{{{ L = 12 }}}
and, also
{{{ L = ( 28 + 4 ) / 2 }}}
{{{ L = 16 }}}
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If I pick the larger answer, then
(2) {{{ W = 28 - L }}}
(2) {{{ W = 28 - 16 }}}
(2) {{{ W = 12 }}}
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These are the answers, because if I picked {{{ L = 12 }}},
then I would get {{{ W = 16 }}} for the width
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The length is 16 cm
The width is 12 cm