Question 50826
The length of a rectangle is 1 cm longer than its width. If the diagonal of the rectangle is 4 cm, what are the dimensions (the length and the width) of the rectangle?

so we will have to right triangles:
edges will have x and x+1 lenght

and their squares' sum will equal to the square of 4.

{{{x^2+x^2+2x+1=16}}}
{{{2x^2+2x+1=16}}}
{{{x^2+x+(1/2)=8}}}
{{{x^2+x+(1/4)=8-(1/4)}}}
{{{(x+(1/2))^2= (31/4)}}}
{{{x+(1/2)= sqrt(31)/2}}}
{{{x = (sqrt(31)-1)/2}}}

this was the short edge

{{{y=x+1}}}
{{{y =  (sqrt(31)+1)/2}}}

this is the long one