Question 938083
{{{drawing(400,240,-1,9,-1,5,
locate(3.5,0,matrix(1,2,8,cm)),locate(8.1,2,matrix(1,2,4,cm)), 
line(0,0,8,0),
line(8,0,8,4),green(locate(4,2.5,D)),
line(8,4,0,4),
line(0,4,0,0),green(line(0,0,8,4)) )}}}
<pre>
The green line labeled <b><font color="green">D</b></font> is the diagonal.  Let's erase the left 
and top sides of the rectangle, like this:

{{{drawing(400,240,-1,9,-1,5,green(locate(4,2.5,D)),
locate(3.5,0,matrix(1,2,8,cm)),locate(8.1,2,matrix(1,2,4,cm)), 
line(0,0,8,0),
line(8,0,8,4), green(line(0,0,8,4)) )}}}

Now as you see, we only have a right triangle and its hypotenuse
is D.  So we use the Pythagorean theorem:

<b><font color="green">D</b></font>² = 8² + 4²
<b><font color="green">D</b></font>² = 64 + 16
<b><font color="green">D</b></font>² = 80
 <b><font color="green">D</b></font> = {{{sqrt(80)}}}

You can either do that with a calculator and get

<b><font color="green">D</b></font> = 8.94427191 cm., rounding it 
off as your teacher requires.

Or else you can give the exact answer in radical form:

<b><font color="green">D</b></font> = {{{sqrt(80)=sqrt(16*5)=sqrt(16)sqrt(5)=4sqrt(5)}}} cm 

Edwin</pre>