<PRE><B>Question 1098166</B>
&lt;br&gt;In the beginning, when we read this problem, we recognize that we need to find two numbers whose difference is 20 and whose product it 5376.  Since it looks like that would be hard, let&#39;s see what algebra could do to help us.&lt;br&gt;
Let x be the width, so x+20 is the length.  Then
{{{x(x+20) = 5376}}}
{{{x^2+20x = 5376}}}
{{{x^2+20x-5376 = 0}}}&lt;br&gt;
If we try to solve this by factoring, what we need to do is find two numbers whose difference is 20 and whose product is 5376.&lt;br&gt;
BUT THAT&#39;S WHAT THE PROBLEM TOLD US TO START WITH!!!&lt;br&gt;
So using algebra didn&#39;t get us any closer to the solution....&lt;br&gt;
Well... we can still use the quadratic formula to solve for x:
{{{x = (-b+-sqrt(b^2-4ac))/2a}}}
{{{x = (-20+-sqrt(400+21504))/2}}}   &lt;-- some ugly arithmetic there...
{{{x = (-20+-sqrt(21904))/2}}}&lt;br&gt;
And now we have to use a calculator to find that square root...
{{{x = (-20+-148)/2}}}  [obviously for this problem we want the positive root]
{{{x = 128/2 = 64}}}&lt;br&gt;
So the width x is 64 and the length x+20 is 84.
Check: 64*84 = 5376&lt;br&gt;
That was a lot of work....&lt;br&gt;
So let&#39;s go back and look at the original problem again and see if we can get to this answer with a lot less work by using logical analysis.&lt;br&gt;
Once again, we need to find two numbers whose difference is 20 and whose product is 5376.&lt;br&gt;
Let&#39;s think about what kinds of numbers we get when we multiply two numbers whose difference is 20.  The difference of 20 means the units digits of the two numbers are the same.  The units digit of our product is 6.  So what single digits can we multiply by themselves to get a units digit of 6?  There are two possibilities: 4 or 6.&lt;br&gt;
Next think about the whole product, 5376.  The square root of 5376 is 70-something, because 70 squared is 4900 and 80 squared is 6400.&lt;br&gt;
So if we want to multiply two numbers whose difference is 20 and whose product is 5376, then the two numbers have to be 60-something and 80-something.&lt;br&gt;
Now we just use trial and error:
66*86 = 5676  nope...
64*84 = 5376  YES!!&lt;br&gt;
So by logical analysis and a bit of estimation, we have found the solution to the problem -- and with a lot less work than using formal algebra.</PRE>