Question 941066
given:
 a rectangle of perimeter {{{P=30cm}}} and 
lengths of sides in the ratio {{{1 : 2}}}

{{{P=2(L+W)}}}
=>{{{30cm=2(L+W)}}}
=>{{{15cm=L+W}}}
=>{{{L=15cm-W}}}................eq.1

if  the ratio of sides lengths {{{1 : 2}}}, then

{{{W:L=1 : 2}}}
=>{{{2W=1L}}}
=>{{{L=2W}}}................eq.2

from eq.1 and eq.2, we have

{{{15cm-W=2W}}}.........solve for {{{W}}}

{{{15cm=2W+W}}}

{{{15cm=3W}}}

{{{highlight(W=5cm)}}}

now find {{{L}}}

{{{L=2W}}}................eq.2

{{{L=2*5cm}}}

{{{highlight(L=10cm)}}}

draw it:


{{{drawing( 600, 600, -1, 20, -10, 20,
line(10,5,10,0),line(0,5,10,5),line(0,5,0,0), 
line(0,0,10,0), graph( 600, 600, -1, 20, -10, 20,  0)) }}}