Question 1012979
.
L=original length; W=original width;P=original perimeter
P2=perimeter of new rectangle
.
{{{P=2(L+W)}}}
{{{42cm=2(L+W)}}}
{{{21=L+W}}}
{{{21-W=L}}} Use this to substitute below.
.
{{{P2=2(3L+4W+7)}}}
{{{154cm=2(3L+4W+7)}}}
{{{77=3L+4W+7}}}
{{{77=3L+4W+7}}} Substitute for L from above.
{{{77=3(21-W)+4W+7}}} 
{{{70=63-3W+4W}}}
{{{7=W}}}
.
ANSWER 1: The original width was 7 cm.
.
{{{L=21-W}}}={{{21-7=14}}}
ANSWER 2: The original length was 14 cm.
.
CHECK:
.
{{{P=2(L+W)}}}
{{{P=2(14cm+7cm)}}}
{{{42cm=2(21cm)}}}
{{{42cm=42cm}}}
.
{{{P2=2(3L+(4W+7))}}}
{{{154cm=2(3(14cm)+4(7cm)+7cm)}}}
{{{154cm=2(42cm+28cm+7cm)}}}
{{{154cm=2(77cm)}}}
{{{154cm=154cm}}}
.