Question 934917
The two rectangles are similar find the length of side x the smaller one has a width of 4 and a length of 16 then the enlarged one has a width of 8 and a length of x how would I do this?
<pre>
{{{drawing(400,100,-8,12,-2,3,locate(3.7,0,length=x),
locate(-2.8,1,width=4),locate(-7.5,0,length=16),locate(9.2,1.5,width=8),
rectangle(-8,0,-3,1), rectangle(1,0,9,2) )}}}

The easy way is to realize that to keep the proportion,
if you double the width, you also have to double the length.

Answer: length = twice 16 or 32.

The harder way (but the only way for harder problems),
is to set up a proportion:

{{{matrix(1,3, 

matrix(1,5,LENGTH,OF,THE,LARGER,RECTANGLE)/matrix(1,5,LENGTH,OF,THE,SMALLER,RECTANGLE),""="", matrix(1,5,WIDTH,OF,THE,LARGER,RECTANGLE)/matrix(1,5,WIDTH,OF,THE,SMALLER,RECTANGLE))}}}

   {{{x/16}}}{{{""=""}}}{{{8/4}}}

Cross-multiply:

   {{{4*x}}}{{{""=""}}}{{{8*16}}}
   {{{4x}}}{{{""=""}}}{{{128}}}
   {{{4x/4}}}{{{""=""}}}{{{128/4}}} 
   {{{x}}}{{{""=""}}}{{{32}}} 

-----------------------------------

You can also set up the proportion this way:   

{{{matrix(1,3, 

matrix(1,5,LENGTH,OF,THE,LARGER,RECTANGLE)/matrix(1,5,WIDTH,OF,THE,LARGER,RECTANGLE),""="", matrix(1,5,LENGTH,OF,THE,SMALLER,RECTANGLE)/matrix(1,5,WIDTH,OF,THE,SMALLER,RECTANGLE))}}}

   {{{x/8}}}{{{""=""}}}{{{16/4}}}

Cross-multiply:

   {{{4*x}}}{{{""=""}}}{{{16*8}}}
   {{{4x}}}{{{""=""}}}{{{128}}}
   {{{4x/4}}}{{{""=""}}}{{{128/4}}} 
   {{{x}}}{{{""=""}}}{{{32}}}

Answer: length of larger rectangle = x = 32 

{{{drawing(400,100,-8,12,-2,3,locate(3.7,0,length=red(32)),
locate(-2.8,1,width=4),locate(-7.5,0,length=16),locate(9.2,1.5,width=8),
rectangle(-8,0,-3,1), rectangle(1,0,9,2) )}}}


Edwin</pre>