Question 73993
Let L=length, w=width. 
The length and width can be represented as
{{{L=w+1}}}
The diagonal of the rectangle is the hypotenuse of the triangle with legs of L and w. So the length and width can be found by Pythagoreans theorem.
{{{(L)^2+w^2=5^2}}}Plug in w+1 into L
{{{(w+1)^2+w^2=25}}}foil the (w+1)^2 term
{{{w^2+2w+2+w^2=25}}}Combine like terms and get everything to one side
{{{2w^2+2w-24=0}}}
Plug this into the quadratic equation to solve for w
*[invoke quadratic "w", 2, 2, -24 ]
This means the width is 3 (the negative width is ignored since it's not practical). So the length is
{{{L=w+1}}}
{{{L=3+1}}}
{{{L=4}}}
So the dimensions are: Width=3,Length=4
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Check:
{{{3^2+4^2=5^2}}}
{{{9+16=25}}}
{{{25=25}}}Works