Question 625527
The straightforward way is:
Let {{{ L }}} = length
Let {{{ W }}} = width
given:
Area = {{{ 100 }}}
(1) {{{ L*W = 100 }}}
(2) {{{ L/W = 4/3 }}}
---------------
Multiply both sides of (2) by {{{ 3W }}}
(2) {{{ 3L = 4W }}}
(2) {{{ L = (4/3)*W }}}
Plug this result into (1)
(1) {{{ (4/3)*W*W = 100 }}}
(1) {{{ (4/3)*W^2= 100 }}}
(1) {{{ W^2 = (3/4)*100 }}}
(1) {{{ W^2 = 75 }}}
(1) {{{ W = sqrt(75) }}}
(1) {{{ W = 5*sqrt(3) }}}
and
(2) {{{ L = (4/3)*W }}}
(2) {{{ L = (4/3)*5( sqrt(3) ) }}}
(2) {{{ L = ( 20*sqrt(3) ) / 3 }}}
check answers:
(1) {{{ L*W = 100 }}}
(1) {{{ (( 20*sqrt(3) ) / 3 )*( 5*sqrt(3) ) = 100 }}}
(1) {{{ sqrt(3) * sqrt(3) * ( 20  / 3 ) * 5 = 100 }}}
(1) {{{ 3*( 100/3) = 100 }}}
(1) {{{ 100 = 100 }}}
and, also:
(2) {{{ L/W = 4/3 }}}
(2) {{{ (( 20*sqrt(3) ) / 3) / (5*sqrt(3)) = 4/3 }}}
(2) {{{ (20/3) / 5 = 4/3 }}}
(2) {{{ 4/3 = 4/3 }}}
OK