Question 75835
Let x=width
Then x+1=length

When we draw the diagonal of a rectangle we, in effect, draw the hypotenuse of two identical right triangles whose sides are the length and width of the rectangle. We can therefore apply the Pythagorean Theorem: 

{{{a^2+b^2=c^2}}} or

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

{{{x^2+x^2+2x+1=16}}} subtract 16 from both sides

{{{2x^2+2x+1-16=16-16}}}
{{{2x^2+2x-15=0}}}  quadratic in standard form

We will 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( 4+120))/(4) }}} 
{{{x = (-2 +- (11.136))/(4) }}}
{{{x = (-2 +(11.136))/(4) }}}
{{{x = (9.136)/(4) }}}


{{{x=2.284}}} cm------------------------width
{{{x+1=2.284+1=3.384}}}cm-----------------------length

We will ignore the negative value for x ( lengths and widths are positive)


CK

{{{(2.284)^2+(3.284)^2=4^2}}}
{{{5.217+10.784=16}}}

{{{16=16}}}


Hope this helps------ptaylor