Question 661498
{{{ P = 2L + 2W }}}
{{{ 66 = 2L + 2W }}}
(1) {{{ 33 = L + W }}} ft
and
{{{ A = 216 }}} ft2
(2) {{{ L*W = 216 }}}
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(1) {{{ W = 33 - L }}}
Substitute (1) into (2)
(2) {{{ L*( 33 - L ) = 216 }}}
(2) {{{ 33L - L^2 = 216 }}}
(2) {{{ -L^2 + 33L - 216 }}}
Solve using the quadratic equation
{{{ L = (-b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = -1 }}}
{{{ b = 33 }}}
{{{ c = -216 }}}
{{{ L = (-33 +- sqrt( 33^2 - 4*(-1)*(-216) )) / (2*(-1)) }}}
{{{ L = (-33 +- sqrt( 1089 - 864 )) / (-2) }}}
{{{ L = (-33 +- sqrt( 225 )) / (-2) }}}
{{{ L = (-33 + 15) / (-2) }}}
{{{ L = (-18) / (-2) }}}
{{{ L = 9 }}}
and
{{{ L = (-33 - 15) / (-2) }}}
{{{ L = (-48) / (-2) }}}
{{{ L = 24 }}}
Note that {{{ 9*24 = 216 }}}
I'll say {{{ L = 24 }}}, and
(1) {{{ 33 = L + W }}}
(1) {{{ 33 = 24 + W }}}
(1) {{{ W = 9 }}}
The width is 9' and the length is 24'