Question 857637
Let the lengths = {{{ a }}}, {{{ b }}},  and {{{ c }}}
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(1) {{{ a + b + c = 48 }}}
(2) {{{ b = 2a }}}
(3) {{{ c = (1/5)*a }}}
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Substitute (2) and (3) into (1)
(1) {{{ a + 2a + (1/5)*a = 48 }}}
(1) {{{ 3a + (1/5)*a = 48 }}}
Multiply both sides by {{{ 5 }}}
(1) {{{ 15a + a = 240 }}}
(1) {{{ 16a = 240 }}}
(1) {{{ a = 15 }}}
and
(2) {{{ b = 2a }}}
(2) {{{ b = 30 }}}
and
(3) {{{ c = (1/5)*15 }}}
(3) {{{ c = 3 }}}
the 3rd length is 3 ft
check:
(1) {{{ a + b + c = 48 }}}
(1) {{{ 15 + 30 + 3 = 48 }}}
(1) {{{ 48 = 48 }}}