Question 100153: Geomatry. The length of a rectangle is 1 cm longer than its width. If the diagnonal of the rectangle is 4cm what are the dimensions (the length and teh width) of the rectangle?
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! The statement that the "length is 1 cm longer than the width" means that we can define the length (l) = w + 1. Width (w) is simply = to w. So, the rectangle has sides of w, w+1, w, and w+1. The diagonal is known to be 4 cm (given).
Now we simply apply the Pythagorean formula. Let's call the diagonal d. That means
Therefore, 
Of course,  is the square of the diagonal, and we were told the diagonal was 4 cm, so  .
Substituting what we know:
Subtracting 16 from both sides:
This does not factor easily, so you can use the quadratic equation to find w.
Quadratic formula: 
Substituing, we have 
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