Question 575365
{{{ P = 2W + 2L }}}
{{{ A = W*L }}}
given:
{{{ P = 140 }}} m
{{{ A = 1200 }}} m2
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(1) {{{ 140 = 2W + 2L }}}
(2) {{{ 1200 = W*L }}}
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(2) {{{ W = 1200/L }}}
Substitute (2) into (1)
(1) {{{ 140 = 2*( 1200/L ) + 2L }}}
Multiply both sides by {{{ L }}}
(1) {{{ 140L = 2400 + 2L^2 }}}
(1) {{{ 2L^2 - 140L + 2400 }}}
(1) {{{ L^2 - 70L + 1200 }}}
Use quadratic equation
{{{L = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{ a = 1 }}}
{{{ b = -70 }}}
{{{ c = 1200 }}}
{{{L = (-(-70) +- sqrt( (-70)^2-4*1*1200 ))/(2*1) }}}
{{{L = ( 70 +- sqrt( 4900 - 4800 )) / 2 }}}
{{{L = ( 70 +- sqrt( 100  )) / 2 }}} 
{{{ L = ( 70 + 10 ) / 2 }}}
{{{ L = 40 }}}
and
(2) {{{ W = 1200/L }}}
(2) {{{ W = 1200/40 }}}
(2) {{{ W = 30 }}}
The length is 40 m 
The width is 30 m