Question 627499
You are mistaken about perimeter.
Remember that in a rectangle, there are:
2 long sides plus
2 short sides which gives me
4 sides total
So the formula for perimeter is
{{{ P = 2L + 2W }}}
You are given {{{ P = 120 }}} ft
{{{ 120 = 2L + 2W }}}
Divide through by {{{2}}}
(1) {{{ 60 = L + W }}}
also
(2) {{{ 4W + 3L = 204 }}}
-------------------------
(1) {{{ W = 60 - L }}}
Substitute (1) into (2)
(2) {{{ 4*( 60 - L ) + 3L = 204 }}}
(2) {{{ 240 - 4L + 3L = 204 }}}
(2) {{{ -L = -36 }}}
(2) {{{ L = 36 }}}
and, since
(1) {{{ W = 60 - L }}}
(1) {{{ W = 60 - 36 }}}
(1) {{{ W = 24 }}}
The length is 36 ft
The width is 24 ft
check:
(2) {{{ 4W + 3L = 204 }}}
(2) {{{ 4*24 + 3*36 = 204 }}}
(2) {{{ 96 + 108 = 204 }}}
(2) {{{ 204 = 204 }}}
OK