Answer:

<em>a</em> = -10 and <em>b</em> = 18. 
Step-by-step explanation:
Let <em>w</em> represent the width of the rectangle. 
We are given that the perimeter of the rectangle is 20 cm, this means that: 

Let's put <em>w</em> in terms of <em>x</em>. Divide both sides by two: 

And solve for <em>w:</em>
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So, the rectangle measures <em>x</em> by (10 -<em> x</em>) cm. 
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According to the Pythagorean Theorem: 

<em>a</em> and <em>b</em> are the legs and <em>c</em> is the hypotenuse. 
Substitute <em>x</em> for <em>a, w</em> for <em>b</em>, and 8 for <em>c:</em>
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Simplify and substitute:

Square: 

Isolate the equation. So: 

Since the leading coefficient is one, divide both sides by two: 

Therefore, <em>a</em> = -10 and <em>b</em> = 18.