Example 3: Find the value of the missing leg and hypotenuse on a scratch piece of paper then fill in the blanks below.

• The Pythagorean Theorem is ______?______
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a2 + b2 = c2
• Substitute x in for the length of the missing leg and x + 1 for the length of the hypotenuse. ____?____
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a2 + x2 = (x + 1)2
• Substitute the known value for a.____?___
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92 + x2 = (x + 1)2
• Simplify.  ________?________
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81 + x2 = x2 + 2x + 1
• Use the subtraction property to isolate.___?_____
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81 - 1 + x2 - x2 = x2 + 2x + 1 - 1
• Simplify. _____?_____
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80 = 2x
• Solve for x .____?_____
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40 = x
• One leg has a length of ___?___ and the other leg has a length of ___?___.
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9, 40
• The hypotenuse has a length of  ____?____
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x + 1 = 40 + 1 = 41