Question 559974
Given:
(1) {{{ L = 2W + 2 }}} ft
also
The formula for Perimeter is
{{{ P = 2W + 2L }}}
Given:
{{{ P = 136 }}} ft
(2) {{{ 2W + 2L = 136 }}}
--------------------
(1) {{{ L = 2W + 2 }}}
(1) {{{ 2W - L = -2 }}}
Subtract (1) from (2)
(2) {{{ 2W + 2L = 136 }}}
(1) {{{ -2W + L = 2 }}}
{{{ 3L = 138 }}}
{{{ L = 46 }}}
and, since
(1) {{{ L = 2W + 2 }}}
(1) {{{ 2W = L - 2 }}}
(1) {{{ W = (1/2)*( L - 2 ) }}}
(1) {{{ W = (1/2)*( 46 - 2 ) }}}
(1) {{{ W = 44/2 }}}
(1) {{{ W = 22 }}}
The room's dimensions are 22' x 46'
check:
{{{ P = 2W + 2L }}}
{{{ 136 = 2*22 + 2*46 }}}
{{{ 136 = 44 + 92 }}}
{{{ 136 = 136 }}}
OK
(1) {{{ L = 2W + 2 }}}
(1) {{{ 46 = 2*22 + 2 }}}
(1) {{{ 46 = 44 + 2 }}}
(1) {{{ 46 = 46 }}}
OK