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Jasper takes a sheet of paper and makes a diagonal cut from one corner to the opposite corner, making two triangles. The cut he makes is 8585 inches long and the width of the paper is 5151 inches. What is the paper's length?\newline_________\_\_\_\_\_\_\_\_\_ inches

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Pythagorean Theorem and its converseright chevron icon

Full solution

Q. Jasper takes a sheet of paper and makes a diagonal cut from one corner to the opposite corner, making two triangles. The cut he makes is 8585 inches long and the width of the paper is 5151 inches. What is the paper's length?\newline_________\_\_\_\_\_\_\_\_\_ inches
  1. Identify Triangle Components: Jasper's cut forms the hypotenuse of a right triangle, where the width is one leg and the length we need to find is the other leg.
  2. Apply Pythagorean Theorem: Using the Pythagorean Theorem: hypotenuse2=width2+length2\text{hypotenuse}^2 = \text{width}^2 + \text{length}^2.
  3. Substitute Values: Plugging in the values: 852=512+length285^2 = 51^2 + \text{length}^2.
  4. Calculate Squares: Calculating the squares: 7225=2601+length27225 = 2601 + \text{length}^2.
  5. Subtract Values: Subtract 26012601 from both sides: 7225−2601=length27225 - 2601 = \text{length}^2.
  6. Solve for Length: Solving for length2\text{length}^2: 4624=length24624 = \text{length}^2.
  7. Take Square Root: Taking the square root of both sides: length=4624length = \sqrt{4624}.
  8. Final Calculation: Calculating the square root: length=68length = \sqrt{68}.

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