Question 1172906
Rectangles A and B are both four times as long as they are wide.
<pre>
They are similar (have the same shape)

Let w = the small rectangle's width.
Then 4w = the small rectangle's length.
</pre>the length of rectangle A is three times the length of rectangle B<pre>
Since 4w = the small rectangle's length,
3(4w) or 12w = the length of the large rectangle's length.

Since the rectangles are similar, the width of the larger triangle is
also three times the width of the smaller rectangle.

So 3w = the width of the larger rectangle.
</pre>If the difference in the perimeters is 16cm,<pre>

The formula for the perimeter is {{{2*length+2*width}}}

{{{(2(12w)^"" + 2(3w))-(2(4w)^"" + 2(w))=16}}}
  
{{{(24w+6w)-(8w+2w)=16}}}

{{{30w - 10w = 16}}}

{{{20w=16}}}

{{{w=16/20}}}

{{{w=4/5}}}

So the width of the smaller rectangle B is 4/5 = 0.8 cm

4w = the small rectangle's length = 4(4/5) = 16/5 - 3.2 cm

3w = the width of the larger rectangle = 3(4/5) = 12/5 = 2.4 cm

12w = the length of the large rectangle's length = 12(4/5) = 48/5 = 9.6 cm

{{{system(L=4W, l=4w,(2W+2L)-(2w+2l)=16, L=3l)}}}

{{{drawing(400,5400/17,-2,11.6,-2,8.8,locate(1.4,6,3.2), locate(3.3,6.8,0.8),
locate(4.8,0,9.6), locate(9.7,1.2,2.4),
line(0,0,9.6,0), line(9.6,0,9.6,2.4), line(9.6,2.4,0,2.4), line(0,0,0,2.4),

line(0,6,3.2,6), line(3.2,6,3.2,6.8),line(3.2,6.8,0,6.8), line(0,6.8,0,6) )}}}

Edwin</pre>