Question 957614
W=width; L=length=5W-3; P=perimeter
Original rectangle:
P=2(L+W) Substitute for L
P=2((5W-3)+W)=6W-3=12W-6
Original perimeter is 12W-6
New rectangle:
{{{W[n]=3W}}}; {{{L[n]=2L}}}={{{10W-6}}}
{{{P[n]=2(W[n]+L[n]) Substitute with W
{{{P[n]=2(3W+10W-6)}}}={{{2(13W-6)=26W-12}}}
New perimeter is 26W-12
New perimeter-original perimeter=92 cm
{{{P[n]-P=92cm}}}
{{{(26W-12)-(12W-6)=92cm}}}
{{{14W-6=92cm}}}
{{{14W=98cm}}}
{{{W=7cm}}} The original width was 7cm.
L=5W-3=5(7cm)-3=35cm-3cm=32cm The original length was 32cm.
Area=L*W=32cm*7cm=224 sq cm
ANSWER: The area of the original rectangle is 224 square centimeters.
CHECK
New Perimeter-Original Perimeter=92cm
2(2L+3W)-2(L+W)=92cm
2(64cm+21cm)-2(32cm+7cm)=92cm
2(85cm)+2(39cm)=92cm
170cm-78cm=92cm
92cm=92cm