Question 531717
(1) {{{ L = 2W - 5 }}}
{{{ A = 33 }}}
{{{ L*W = 33 }}}
(2) {{{ W = 33/L }}}
Substitute (2) into (1)
(1) {{{ L = 2*(33/L) - 5 }}}
(1) {{{ L^2 = 66 - 5L }}}
(1) {{{ L^2 + 5L - 66 = 0 }}}
Use quadratic formula
{{{L = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{ a = 1 }}}
{{{ b = 5 }}}
{{{ c = -66 }}}
{{{L = (-5 +- sqrt( 5^2-4*1*(-66) ))/(2*1) }}}
{{{L = (-5 +- sqrt( 25 + 264 ))/2 }}}
{{{L = (-5 +- sqrt( 289 ))/2 }}}
{{{L = (-5 + 17)/2 }}}
{{{ L = 12/2 }}}
{{{ L = 6 }}} ( ignore the negative root )
(2) {{{ W = 33/L }}}
(2) {{{ W = 33/6 }}}
(2) {{{ W = 5.5 }}}
The dimensions are 5.5 m x 6 m
check:
(1) {{{ L = 2*(33/L) - 5 }}}
(1) {{{ 6 = 2W - 5 }}}
(1) {{{ 6 = 2*5.5 - 5 }}}
(1) {{{ 6 = 11 - 5 }}}
(1) {{{ 6 = 6 }}}
OK