Question 90301
YOU WERE ALMOST THERE!!!!!!!!!!!!!!!
Let x=width
Then x+1=length

x^2+(x+1)^2=4^2  get rid of parens

x^2+x^2+2x+1=16
2x^2+2x+1-16=0

2x^2+2x-15=0  quadratic in standard form.  We can solve using the quadratic formula

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{x = (-2 +- sqrt( 2^2-4*2*(-15) ))/(2*2) }}}  

{{{x = (-2 +- sqrt(124))/(4) }}} 

We'll not worry about the negative value for x, since lengths and widths are positive
{{{x = (-2 + 11.1355)/(4) }}} 
{{{x = (9.1355)/(4) }}} 

{{{x = 2.284 }}}cm----------------------width

{{{x+1=2.284+1=3.284}}}cm-----------------length

CK

{{{2.284^2+3.284^2=4^2}}} 
{{{5.216+10.785=16}}}

16.001~~16


Hope this helps---ptaylor